Basic

📁 Source: Mathlib/Algebra/Category/ModuleCat/Basic.lean

Statistics

Metric	Count
Definitions toLinearEquiv, toModuleIso, instLinear, instModuleCarrier, hom, hom, hom', hom₂, instModule, carrier, endRingEquiv, equivalenceSemimoduleCat, hasForgetToAddCommGroup, homAddEquiv, homEquiv, homLinearEquiv, homMk, instAddCommGroupCarrierMkOfSMul', instAddCommGroupHom, instAddHom, instCoeSortType, instConcreteCategoryLinearMapIdCarrier, instInhabited, instLinear, instModuleCarrierMkOfSMul', instNegHom, instPreadditive, instSMulCarrierMkOfSMul', instSMulHom, instSMulIntHom, instSMulNatHom, instSubHom, instZeroHom, isAddCommGroup, isModule, mkOfSMul, mkOfSMul', moduleCategory, of, ofHom, ofHom₂, smul, smulNatTrans, «term↟_», linearEquivIsoModuleIso	45
Theorems toLinearEquiv_apply, toLinearEquiv_symm, toLinearMap_toLinearEquiv, toModuleIso_hom, toModuleIso_inv, comp_id_moduleCat, id_moduleCat_comp, instIsScalarTowerCarrier, instSMulCommClassCarrier, ext, ext_iff, hom₂_apply, hom₂_ofHom₂, conj_eq_conj, homCongr_eq_arrowCongr, coe_of, comp_apply, endRingEquiv_apply, endRingEquiv_symm_apply_hom, forget_map, forget_obj, forget₂_addCommGrp_additive, forget₂_map, forget₂_map_homMk, forget₂_obj, forget₂_obj_moduleCat_of, homAddEquiv_apply, homAddEquiv_symm_apply_hom, homLinearEquiv_apply, homLinearEquiv_symm_apply, homMk_hom_apply, hom_add, hom_bijective, hom_comp, hom_ext, hom_ext_iff, hom_id, hom_injective, hom_inv_apply, hom_neg, hom_nsmul, hom_ofHom, hom_smul, hom_sub, hom_sum, hom_surjective, hom_zero, hom_zsmul, id_apply, instHasZeroObject, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, instReflectsIsomorphismsForgetLinearMapIdCarrier, inv_hom_apply, isZero_iff_subsingleton, isZero_of_iff_subsingleton, isZero_of_subsingleton, mkOfSMul'_smul, mkOfSMul_smul, ofHom_apply, ofHom_comp, ofHom_hom, ofHom_id, ofHom₂_hom_apply_hom, ofHom₂_hom₂, of_coe, smulNatTrans_apply_app, smul_naturality, subsingleton_of_isZero, linearEquivIsoModuleIso_hom, linearEquivIsoModuleIso_inv	70
Total	115

CategoryTheory.Iso

Definitions

Name	Category	Theorems
toLinearEquiv 📖	CompOp	6 math math: ModuleCat.Iso.homCongr_eq_arrowCongr, toLinearEquiv_symm, toLinearEquiv_apply, ModuleCat.Iso.conj_eq_conj, linearEquivIsoModuleIso_inv, toLinearMap_toLinearEquiv

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
toLinearEquiv_apply 📖	mathematical	—	DFunLike.coe LinearEquiv Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids ModuleCat.carrier AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule EquivLike.toFunLike LinearEquiv.instEquivLike toLinearEquiv CategoryTheory.ConcreteCategory.hom ModuleCat ModuleCat.moduleCategory LinearMap LinearMap.instFunLike ModuleCat.instConcreteCategoryLinearMapIdCarrier hom	—	RingHomInvPair.ids
toLinearEquiv_symm 📖	mathematical	—	LinearEquiv.symm ModuleCat.carrier Ring.toSemiring AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids toLinearEquiv symm ModuleCat ModuleCat.moduleCategory	—	RingHomInvPair.ids
toLinearMap_toLinearEquiv 📖	mathematical	—	LinearEquiv.toLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids ModuleCat.carrier AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule toLinearEquiv ModuleCat.Hom.hom hom ModuleCat ModuleCat.moduleCategory	—	RingHomInvPair.ids

LinearEquiv

Definitions

Name	Category	Theorems
toModuleIso 📖	CompOp	8 math math: linearEquivIsoModuleIso_hom, toModuleIso_inv, ModuleCat.MonoidalCategory.rightUnitor_def, ModuleCat.MonoidalCategory.associator_def, inhomogeneousCochains.d_eq, ModuleCat.MonoidalCategory.leftUnitor_def, groupHomology.inhomogeneousChains.d_eq, toModuleIso_hom

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
toModuleIso_hom 📖	mathematical	—	CategoryTheory.Iso.hom ModuleCat ModuleCat.moduleCategory ModuleCat.of toModuleIso ModuleCat.ofHom toLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid	—	RingHomInvPair.ids
toModuleIso_inv 📖	mathematical	—	CategoryTheory.Iso.inv ModuleCat ModuleCat.moduleCategory ModuleCat.of toModuleIso ModuleCat.ofHom toLinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid symm	—	RingHomInvPair.ids

LinearMap

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
comp_id_moduleCat 📖	mathematical	—	comp ModuleCat.carrier Ring.toSemiring AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids ModuleCat.Hom.hom CategoryTheory.CategoryStruct.id ModuleCat CategoryTheory.Category.toCategoryStruct ModuleCat.moduleCategory	—	—
id_moduleCat_comp 📖	mathematical	—	comp ModuleCat.carrier Ring.toSemiring AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids ModuleCat.Hom.hom CategoryTheory.CategoryStruct.id ModuleCat CategoryTheory.Category.toCategoryStruct ModuleCat.moduleCategory	—	—

ModuleCat

Definitions

Name	Category	Theorems
carrier 📖	CompOp	1067 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, Rep.resCoindHomEquiv_symm_apply_hom, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, Rep.resCoindHomEquiv_apply_hom, groupCohomology.instEpiModuleCatH2π, hom_zero, groupHomology.π_comp_H2Iso_hom_assoc, instReflectsIsomorphismsForgetLinearMapIdCarrier, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective, of_coe, forget_preservesLimits, TopModuleCat.hom_zero, CommRingCat.KaehlerDifferential.map_d, MonoidalCategory.braiding_hom_apply, biproductIsoPi_inv_comp_π, FilteredColimits.colimit_smul_mk_eq, groupHomology.mapCycles₂_comp_assoc, restrictScalars.map_apply, forget₂_reflectsLimitsOfSize, groupCohomology.toCocycles_comp_isoCocycles₁_hom, CategoryTheory.linearCoyoneda_obj_obj_carrier, Rep.MonoidalClosed.linearHomEquiv_symm_hom, groupCohomology.isoCocycles₁_hom_comp_i_apply, groupCohomology.mem_cocycles₂_def, ContinuousCohomology.I_obj_V_isAddCommGroup, groupHomology.coinfNatTrans_app, CategoryTheory.Iso.toCoalgEquiv_symm, forget_preservesLimitsOfSize, groupCohomology.d₂₃_hom_apply, LightCondensed.ihomPoints_apply, LinearMap.id_fgModuleCat_comp, groupHomology.d₁₀_single_one, groupHomology.boundaries₂_le_cycles₂, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, FGModuleCat.hom_hom_id, Rep.diagonalSuccIsoFree_inv_hom_single, groupCohomology.d₀₁_comp_d₁₂, Representation.repOfTprodIso_apply, freeHomEquiv_apply, epi_as_hom''_mkQ, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, forget₂AddCommGroup_preservesLimitsOfSize, toMatrixModCat_map, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, LightCondensed.forget_obj_val_map, ContinuousCohomology.I_obj_V_carrier, groupCohomology.cocyclesIso₀_hom_comp_f, Rep.resCoindAdjunction_counit_app_hom_hom, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, groupHomology.d₃₂_single, TopModuleCat.hom_zero_apply, groupCohomology.eq_d₀₁_comp_inv, extendScalarsId_hom_app_one_tmul, groupCohomology.H1π_comp_map_assoc, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, groupCohomology.π_comp_H0Iso_hom, FDRep.endRingEquiv_symm_comp_ρ, groupCohomology.π_comp_H1Iso_hom_assoc, ι_coprodIsoDirectSum_hom_apply, restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, CoalgCat.of_comul, LightCondensed.ihomPoints_symm_comp, isZero_iff_subsingleton, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_carrier, Rep.indToCoindAux_self, groupCohomology.mapCocycles₂_comp_i, AlternatingMap.postcomp_apply, groupHomology.eq_d₃₂_comp_inv, QuadraticModuleCat.toIsometry_comp, Rep.coe_res_obj_ρ, Rep.invariantsFunctor_obj_carrier, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, monoidalClosed_uncurry, Rep.diagonalHomEquiv_symm_apply, groupCohomology.H0IsoOfIsTrivial_hom, CondensedMod.isDiscrete_tfae, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, groupHomology.mem_cycles₂_iff, Iso.homCongr_eq_arrowCongr, CoextendScalars.smul_apply', groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, groupHomology.cyclesMap_comp_isoCycles₂_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, directLimitCocone_pt_carrier, toMatrixModCat_obj_carrier, groupCohomology.d₁₂_hom_apply, instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, groupHomology.comp_d₂₁_eq, PresheafOfModules.pushforward_map_app_apply, CategoryTheory.preadditiveYonedaObj_obj_carrier, groupCohomology.coboundariesToCocycles₁_apply, groupHomology.mapCycles₁_comp_assoc, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, PresheafOfModules.sections_property, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, PresheafOfModules.toSheafify_app_apply', PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, Rep.coinvariantsAdjunction_counit_app, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, QuadraticModuleCat.forget₂_map_associator_inv, LinearMap.comp_id_fgModuleCat, RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, groupCohomology.comp_d₁₂_eq, toMatrixModCat_obj_isAddCommGroup, groupCohomology.mem_cocycles₁_of_addMonoidHom, groupCohomology.cocycles₂.d₂₃_apply, groupCohomology.d₀₁_hom_apply, Rep.linearization_single, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, hom_surjective, TopModuleCat.coe_freeObj, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CoalgCat.tensorObj_isAddCommGroup, forget₂_addCommGrp_essSurj, groupCohomology.dArrowIso₀₁_inv_right, groupCohomology.map_H0Iso_hom_f_apply, groupCohomology.d₁₂_comp_d₂₃_apply, groupCohomology.H0IsoOfIsTrivial_inv_apply, groupCohomology.eq_d₂₃_comp_inv_assoc, PresheafOfModules.congr_map_apply, PresheafOfModules.freeYonedaEquiv_symm_app, Rep.finsuppToCoinvariantsTensorFree_single, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, PresheafOfModules.restrictScalarsObj_map, groupHomology.chains₁ToCoinvariantsKer_surjective, Rep.coinvariantsTensorFreeLEquiv_symm_apply, TopModuleCat.continuousSMul, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, groupHomology.cycles₁_eq_top_of_isTrivial, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Rep.resCoindAdjunction_unit_app_hom_hom, groupHomology.d₃₂_comp_d₂₁_assoc, groupCohomology.mem_cocycles₁_def, endRingEquiv_symm_apply_hom, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, Rep.homEquiv_apply_hom, FilteredColimits.colimit_zero_eq, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, PresheafOfModules.pushforward₀_obj_obj_carrier, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MonoidalCategory.associator_hom_apply, groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂, CategoryTheory.Iso.toCoalgEquiv_toCoalgHom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, Rep.norm_comm_apply, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasLimit.productLimitCone_cone_π, HasColimit.colimitCocone_ι_app, CoalgCat.moduleCat_of_toModuleCat, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, groupCohomology.coboundaries₁_eq_bot_of_isTrivial, MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, PresheafOfModules.Derivation.postcomp_d_apply, smulShortComplex_X₃_isAddCommGroup, forget₂_addCommGroup_full, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, PresheafOfModules.Derivation.d_one, groupCohomology.cocycles₂_map_one_fst, PresheafOfModules.sectionsMap_coe, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.ρ_hom, Rep.diagonalSuccIsoFree_inv_hom_single_single, groupCohomology.H1IsoOfIsTrivial_inv_apply, PresheafOfModules.Sheafify.map_smul_eq, PresheafOfModules.map_comp_apply, biprodIsoProd_inv_comp_snd_apply, RestrictionCoextensionAdj.counit'_app, groupHomology.chainsMap_f_3_comp_chainsIso₃, PresheafOfModules.pushforward_map_app_apply', groupHomology.mapCycles₁_id_comp_assoc, groupHomology.eq_d₂₁_comp_inv, PresheafOfModules.Derivation.d_mul, isFG_iff, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, CategoryTheory.linearYoneda_obj_obj_carrier, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, groupHomology.mapCycles₁_comp, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Rep.ihom_ev_app_hom, homLinearEquiv_symm_apply, hom_smul, groupCohomology.dArrowIso₀₁_hom_right, uliftFunctorForgetIso_hom_app, Rep.MonoidalClosed.linearHomEquivComm_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom, Rep.coe_linearization_obj, FGModuleCat.hom_comp, ContinuousCohomology.I_obj_ρ_apply, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, imageIsoRange_hom_subtype, GradedObject.finrankSupport_subset_iff, CategoryTheory.Iso.toIsometryEquiv_toFun, groupHomology.mapCycles₁_comp_i, CoextendScalars.smul_apply, groupCohomology.shortComplexH0_f, binaryProductLimitCone_cone_π_app_right, groupCohomology.cocyclesOfIsCocycle₁_coe, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, HasColimit.colimitCocone_pt_isModule, PresheafOfModules.toPresheaf_obj_coe, groupCohomology.coboundaries₂_le_cocycles₂, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, Rep.coindVEquiv_symm_apply_coe, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, imageIsoRange_inv_image_ι_apply, CategoryTheory.preadditiveYonedaMap_app, groupCohomology.comp_d₂₃_eq, CondensedMod.isDiscrete_iff_isDiscrete_forget, PresheafOfModules.map_smul, FGModuleCat.FGModuleCatEvaluation_apply, epi_iff_surjective, groupCohomology.coboundaries₂.val_eq_coe, PresheafOfModules.Monoidal.tensorObj_map_tmul, TopModuleCat.coe_of, exteriorPower.map_mk, TopModuleCat.ofHom_hom, subsingleton_of_isZero, cokernel_π_cokernelIsoRangeQuotient_hom, Rep.ofModuleMonoidAlgebra_obj_coe, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupCohomology.infNatTrans_app, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, hom_inv_apply, groupHomology.mapCycles₂_id_comp, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, monoidalClosed_curry, groupCohomology.d₀₁_apply_mem_cocycles₁, QuadraticModuleCat.instMonoidalCategory.tensorObj_form, CoalgCat.tensorHom_def, Module.Flat.iff_rTensor_preserves_shortComplex_exact, MonoidalCategory.leftUnitor_hom_apply, Rep.indToCoindAux_fst_mul_inv, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.coinvariantsFunctor_obj_carrier, Rep.applyAsHom_comm_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, restrictScalarsId'App_hom_apply, groupCohomology.subtype_comp_d₀₁_apply, ContinuousCohomology.Iobj_ρ_apply, SheafOfModules.pushforwardComp_inv_app_val_app, FilteredColimits.forget_preservesFilteredColimits, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.comp_d₀₁_eq, groupCohomology.cocycles₂_map_one_snd, homAddEquiv_symm_apply_hom, Rep.coinvariantsTensorFreeLEquiv_apply, groupHomology.toCycles_comp_isoCycles₁_hom_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, CategoryTheory.ShortComplex.moduleCatMk_X₃_carrier, groupHomology.mapCycles₂_comp_i, localizedModule_isLocalizedModule, range_eq_top_of_epi, groupCohomology.map_H0Iso_hom_f, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, groupHomology.boundariesOfIsBoundary₁_coe, Derivation.d_mul, Rep.indToCoindAux_comm, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, ContinuousCohomology.I_obj_V_isModule, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, groupHomology.cyclesIso₀_comp_H0π_apply, CoalgCat.associator_def, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, CondensedMod.epi_iff_surjective_on_stonean, hom_whiskerRight, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.exists_d_comp_eq_d, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, hom_inv_associator, FGModuleCat.hom_id, Rep.toAdditive_symm_apply, lof_coprodIsoDirectSum_inv, groupHomology.single_one_fst_sub_single_one_fst_mem_boundaries₂, TopModuleCat.hom_add, BialgCat.forget₂_coalgebra_obj, CoalgCat.MonoidalCategoryAux.tensorObj_comul, CoalgCat.comul_def, inv_hom_apply, forget₂AddCommGroup_preservesLimits, directLimitIsColimit_desc, groupHomology.mapCycles₁_id_comp_apply, MonoidalCategory.rightUnitor_def, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, CategoryTheory.Iso.toLinearEquiv_symm, PresheafOfModules.presheaf_map_apply_coe, smulShortComplex_g, Rep.ofMulDistribMulAction_ρ_apply_apply, PresheafOfModules.Derivation.congr_d, Rep.instIsTrivialCarrierVModuleCatOfCompLinearMapIdρ, groupCohomology.instEpiModuleCatH1π, MonoidalCategory.associator_def, groupCohomology.H2π_comp_map, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, groupHomology.π_comp_H2Iso_hom, forget₂_obj, Rep.indResAdjunction_counit_app_hom_hom, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Rep.coindToInd_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, SheafOfModules.pushforwardCongr_hom_app_val_app, hom_whiskerLeft, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, groupHomology.mapCycles₂_comp, comp_apply, restrictScalarsCongr_hom_app, MonoidalCategory.tensorUnit_carrier, kernelIsoKer_inv_kernel_ι_apply, ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.whiskering_linearYoneda, Rep.coe_of, MonoidalCategory.rightUnitor_hom_apply, groupCohomology.isoCocycles₂_hom_comp_i, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CoalgCat.whiskerRight_def, TopModuleCat.hom_zsmul, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, FilteredColimits.M.mk_map, groupCohomology.π_comp_H0Iso_hom_apply, groupHomology.coe_mapCycles₂, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, CategoryTheory.whiskering_linearCoyoneda₂, FGModuleCat.obj_carrier, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, groupHomology.H1π_comp_map_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, groupCohomology.dArrowIso₀₁_hom_left, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MatrixModCat.toModuleCat_obj_carrier, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, groupCohomology.cocycles₁_map_inv, Rep.freeLiftLEquiv_apply, hom_hom_leftUnitor, groupCohomology.mapCocycles₁_one, PresheafOfModules.surjective_of_epi, adj_homEquiv, instIsScalarTowerLocalizationCarrierLocalizedModule, groupHomology.H2π_comp_map_assoc, Rep.indToCoindAux_mul_fst, hom_hom_rightUnitor, LightCondensed.forget_map_val_app, biprodIsoProd_inv_comp_snd, CoalgCat.tensorUnit_carrier, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, CategoryTheory.Iso.toCoalgEquiv_refl, piIsoPi_inv_kernel_ι_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, Rep.ihom_obj_ρ_apply, ker_eq_bot_of_mono, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, groupHomology.d₁₀ArrowIso_inv_right, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, Rep.finsuppTensorRight_hom_hom, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, groupCohomology.norm_ofAlgebraAutOnUnits_eq, groupCohomology.π_comp_H0Iso_hom_assoc, MonModuleEquivalenceAlgebra.functor_obj_carrier, imageIsoRange_hom_subtype_assoc, groupCohomology.mem_cocycles₂_iff, Rep.tensor_ρ, Rep.toAdditive_apply, QuadraticModuleCat.toIsometry_whiskerRight, PresheafOfModules.pushforward_obj_map_apply, groupCohomology.H2π_comp_map_assoc, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CoalgCat.forget_reflects_isos, Rep.ofDistribMulAction_ρ_apply_apply, groupCohomology.d₀₁_ker_eq_invariants, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, Rep.linearization_η_hom_apply, smulNatTrans_apply_app, FGModuleCat.ihom_obj, TopModuleCat.hom_id, forget_reflectsLimits, Rep.leftRegularHomEquiv_symm_apply, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, PresheafOfModules.forgetToPresheafModuleCatObjObj_coe, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, groupHomology.H1AddEquivOfIsTrivial_single, groupCohomology.mem_cocycles₁_iff, CoalgCat.ofComonObjCoalgebraStruct_comul, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, groupHomology.range_d₁₀_eq_coinvariantsKer, QuadraticModuleCat.toIsometry_tensorHom, PresheafOfModules.unitHomEquiv_apply_coe, groupCohomology.inhomogeneousCochains.d_comp_d, FreeMonoidal.εIso_inv_freeMk, groupHomology.isoCycles₂_hom_comp_i_apply, Rep.ofModuleMonoidAlgebra_obj_ρ, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, QuadraticModuleCat.toIsometry_hom_leftUnitor, Rep.coinvariantsShortComplex_f, SheafOfModules.pushforwardCongr_inv_app_val_app, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, QuadraticModuleCat.toIsometry_hom_rightUnitor, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles, RestrictionCoextensionAdj.unit'_app, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierOfCarrierStalkAbPresheafPrimeComplAsIdealHomToStalk, groupHomology.eq_d₂₁_comp_inv_assoc, imageIsoRange_inv_image_ι, smulShortComplex_X₃_carrier, free_η_freeMk, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, ContinuousCohomology.I_map_hom, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, groupHomology.inhomogeneousChains.d_single, groupCohomology.coboundariesOfIsCoboundary₁_coe, exteriorPower.iso₁_hom_apply, TopModuleCat.freeMap_map, Representation.coind'_apply_apply, groupCohomology.d₁₂_comp_d₂₃_assoc, QuadraticModuleCat.Hom.toIsometry_injective, CoalgCat.Hom.toCoalgHom_injective, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, PresheafOfModules.presheaf_obj_coe, hom_inv_rightUnitor, ExtendScalars.smul_tmul, hom_sum, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, CategoryTheory.Iso.toCoalgEquiv_trans, groupHomology.mapCycles₂_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, Rep.coindIso_inv_hom_hom, hom_nsmul, groupCohomology.map_id_comp_H0Iso_hom_apply, groupCohomology.cocycles₁_map_mul_of_isTrivial, forget_obj, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.chainsMap_id_f_hom_eq_mapRange, PresheafOfModules.toPresheaf_map_app_apply, groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupCohomology.map_id_comp_H0Iso_hom, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, PresheafOfModules.Derivation'.d_app, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mapCycles₁_id_comp, Rep.indToCoindAux_mul_snd, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, coe_of, CategoryTheory.Iso.toIsometryEquiv_refl, QuadraticModuleCat.toIsometry_inv_rightUnitor, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, ExtendScalars.map_tmul, FilteredColimits.colimit_add_mk_eq', QuadraticModuleCat.cliffordAlgebra_map, FilteredColimits.forget_reflectsFilteredColimits, groupCohomology.cocyclesOfIsMulCocycle₂_coe, LinearMap.id_moduleCat_comp, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, QuadraticModuleCat.toIsometry_whiskerLeft, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.Iso.toLinearEquiv_apply, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, Derivation.d_map, groupHomology.isoShortComplexH1_inv, groupCohomology.coboundariesOfIsMulCoboundary₁_coe, SheafOfModules.pushforwardComp_hom_app_val_app, groupHomology.eq_d₁₀_comp_inv_assoc, groupCohomology.d₁₂_comp_d₂₃, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, Rep.linearization_obj_ρ, Rep.toCoinvariantsMkQ_hom, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, MonoidalCategory.tensorObj, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, imageIsoRange_inv_image_ι_assoc, MonoidalCategory.rightUnitor_inv_apply, groupCohomology.H1π_eq_zero_iff, groupHomology.H1AddEquivOfIsTrivial_symm_apply, Rep.invariantsAdjunction_counit_app_hom, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, groupCohomology.coboundaries₁.val_eq_coe, groupHomology.d₃₂_single_one_fst, inhomogeneousCochains.d_hom_apply, CoalgCat.MonoidalCategoryAux.counit_tensorObj, Rep.coind'_ext_iff, CoalgCat.counit_def, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, groupHomology.d₂₁_comp_d₁₀, PresheafOfModules.Elements.fromFreeYoneda_app_apply, binaryProductLimitCone_cone_π_app_left, HasColimit.coconePointSMul_apply, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, kernelIsoKer_hom_ker_subtype, smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, hom_add, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, groupCohomology.cocyclesMk₁_eq, AlgCat.forget₂_module_obj, MonoidalCategory.leftUnitor_inv_apply, ι_coprodIsoDirectSum_hom, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, SheafOfModules.relationsOfIsCokernelFree_I, MonModuleEquivalenceAlgebra.algebraMap, MonoidalCategory.tensorμ_apply, groupHomology.cyclesOfIsCycle₁_coe, Rep.quotientToInvariantsFunctor_obj_V, MonoidalCategory.tensorObj_isModule, groupHomology.inhomogeneousChains.ext_iff, MonoidalCategory.tensorObj_isAddCommGroup, groupHomology.d₂₁_apply_mem_cycles₁, groupCohomology.coboundariesToCocycles₂_apply, ihom_map_apply, MonModuleEquivalenceAlgebra.inverseObj_mul, ihom_coev_app, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.cocyclesOfIsMulCocycle₁_coe, groupCohomology.H2π_eq_zero_iff, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, groupCohomology.mapCocycles₁_comp_i_assoc, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, groupCohomology.cocycles₁.val_eq_coe, TopModuleCat.isTopologicalAddGroup, groupCohomology.H1π_comp_map_apply, free_shortExact, PresheafOfModules.ofPresheaf_obj_carrier, Rep.leftRegularHom_hom_single, groupCohomology.cocycles₁_map_one, groupHomology.eq_d₃₂_comp_inv_assoc, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, hom_hom_associator, CoalgCat.forget₂_obj, groupCohomology.π_comp_H2Iso_hom_assoc, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, Rep.finsuppTensorRight_inv_hom, Rep.coinvariantsMk_app_hom, Rep.ihom_obj_V_isAddCommGroup, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, CategoryTheory.ShortComplex.moduleCat_exact_iff, groupHomology.mapCycles₂_hom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, mkOfSMul_smul, MatrixModCat.isScalarTower_toModuleCat, restrictScalars.smul_def, CoalgCat.whiskerLeft_def, TopModuleCat.hom_sub, kernelIsoKer_hom_ker_subtype_apply, QuadraticModuleCat.toIsometry_id, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, Rep.coindVEquiv_apply_hom, PresheafOfModules.Derivation.d_app, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, groupHomology.H1π_eq_zero_iff, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, groupHomology.π_comp_H1Iso_hom_assoc, LightCondMod.hom_naturality_apply, TopModuleCat.forget₂_TopCat_obj, groupHomology.chainsMap_f_2_comp_chainsIso₂, groupHomology.d₂₁_single_one_fst, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, HasLimit.productLimitCone_cone_pt_isModule, groupHomology.H2π_comp_map, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, TopModuleCat.hom_nsmul, groupCohomology.cocycles₂.val_eq_coe, groupCohomology.eq_d₂₃_comp_inv, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, LightCondensed.ihomPoints_symm_apply, Derivation.d_add, groupHomology.H1π_comp_map_assoc, Rep.ihom_map_hom, groupHomology.instEpiModuleCatH1π, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, groupHomology.H1AddEquivOfIsTrivial_apply, MonoidalCategory.whiskerRight_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, Rep.finsuppTensorLeft_inv_hom, TopModuleCat.instIsTopologicalAddGroupCarrier, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, PresheafOfModules.Derivation'.app_apply, CoalgCat.forget₂_map, groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂, Rep.unit_iso_comm, Rep.leftRegularHomEquiv_symm_single, inhomogeneousCochains.d_eq, HasLimit.productLimitCone_cone_pt_carrier, groupHomology.instEpiModuleCatH2π, piIsoPi_hom_ker_subtype, directLimitDiagram_obj_carrier, hom_id, groupCohomology.cocyclesMk₂_eq, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.H1π_comp_map, groupHomology.chainsMap_f_hom, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, piIsoPi_inv_kernel_ι, Rep.norm_hom, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.indResAdjunction_unit_app_hom_hom, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, groupHomology.boundariesOfIsBoundary₂_coe, groupHomology.cyclesMk₁_eq, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, LightCondensed.ihom_map_val_app, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, TopModuleCat.cokerπ_surjective, FreeMonoidal.μIso_inv_freeMk, uliftFunctor_map, Rep.Action_ρ_eq_ρ, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, ofHom_hom, Rep.coindMap_hom, groupHomology.mapCycles₂_id_comp_apply, Rep.trivial_def, groupCohomology.cocycles₂_ext_iff, instFiniteCarrierObjModuleCatIsFG, Rep.MonoidalClosed.linearHomEquiv_hom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, Rep.invariantsAdjunction_homEquiv_apply_hom, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, localizedModuleMap_hom_apply, Rep.hom_comm_apply, SheafOfModules.pushforwardNatTrans_app_val_app, groupHomology.H2π_comp_map_apply, Hom.hom₂_apply, CategoryTheory.Iso.toIsometryEquiv_invFun, TopModuleCat.hom_smul, HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, uliftFunctor_obj, forget₂_addCommGrp_additive, Module.Flat.iff_preservesFiniteLimits_tensorLeft, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, AlternatingMap.ext_iff, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, CoalgCat.MonoidalCategoryAux.comul_tensorObj, groupCohomology.coboundaries₁_ext_iff, Rep.finsuppTensorLeft_hom_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, projective_of_module_projective, MatrixModCat.toModuleCat_map, MonoidalCategory.leftUnitor_def, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, binaryProductLimitCone_isLimit_lift, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, homLinearEquiv_apply, Rep.coinvariantsTensorMk_apply, TopModuleCat.kerι_apply, Rep.indMap_hom, ContinuousCohomology.I_obj_V_topologicalSpace, groupHomology.isoCycles₁_hom_comp_i_assoc, Rep.homEquiv_symm_apply_hom, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, AlgCat.forget₂_module_map, FilteredColimits.M.mk_surjective, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Rep.invariantsFunctor_map_hom, Iso.conj_eq_conj, groupHomology.d₁₀_eq_zero_of_isTrivial, CoalgCat.toComon_map_hom, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, groupCohomology.d₀₁_comp_d₁₂_assoc, MonoidalCategory.tensorObj_def, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, groupHomology.d₂₁_single_one_snd, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, biprodIsoProd_inv_comp_fst, groupHomology.π_map_apply, CoalgCat.rightUnitor_def, BialgCat.forget₂_coalgebra_map, groupHomology.d₃₂_comp_d₂₁, groupHomology.d₃₂_single_one_snd, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, QuadraticModuleCat.cliffordAlgebra_obj_carrier, groupHomology.π_comp_H2Iso_hom_apply, CoalgCat.tensorObj_carrier, SheafOfModules.relationsOfIsCokernelFree_s, forget₂_reflectsLimits, FDRep.of_ρ, forget₂PreservesColimitsOfShape, MatrixModCat.toModuleCat_obj_isAddCommGroup, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, Rep.ihom_coev_app_hom, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, Rep.leftRegularHomEquiv_apply, restrictScalars.smul_def', PresheafOfModules.pushforward_obj_map_apply', groupHomology.isoCycles₁_inv_comp_iCycles, free_shortExact_rank_add, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, FGModuleCat.FGModuleCatEvaluation_apply', forget₂AddCommGroup_reflectsLimit, groupHomology.isoShortComplexH2_inv, groupHomology.coe_mapCycles₁, groupHomology.toCycles_comp_isoCycles₁_hom, HasLimit.productLimitCone_cone_pt_isAddCommGroup, hom_inv_leftUnitor, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, groupCohomology.d₀₁_comp_d₁₂_apply, free_map_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, Representation.linHom.mem_invariants_iff_comm, groupHomology.mapCycles₂_comp_i_apply, binaryProductLimitCone_cone_pt, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ofHom₂_hom_apply_hom, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, groupHomology.boundariesToCycles₂_apply, groupCohomology.subtype_comp_d₀₁, MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, groupHomology.cyclesOfIsCycle₂_coe, Rep.freeLift_hom, groupHomology.isoCycles₂_hom_comp_i, CoalgCat.tensorObj_instCoalgebra, groupHomology.π_comp_H1Iso_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.π_map_apply, Rep.indToCoindAux_snd_mul_inv, hom_sub, CoalgCat.ofComonObjCoalgebraStruct_counit, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, Rep.res_obj_ρ, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, ofHom₂_compr₂, Algebra.instSMulCommClassCarrier, PresheafOfModules.freeYonedaEquiv_comp, forget₂AddCommGroup_preservesLimit, groupCohomology.coboundaries₁_le_cocycles₁, Rep.ihom_obj_V_isModule, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, CoalgCat.tensorObj_isModule, FreeMonoidal.εIso_hom_one, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, groupHomology.d₁₀ArrowIso_hom_right, QuadraticModuleCat.toIsometry_inv_leftUnitor, Rep.freeLift_hom_single_single, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, groupHomology.single_one_mem_boundaries₁, mono_iff_ker_eq_bot, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, groupHomology.π_comp_H1Iso_inv_apply, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.isoCocycles₂_hom_comp_i_apply, extendRestrictScalarsAdj_unit_app_apply, hom_bijective, Rep.diagonalHomEquiv_apply, groupHomology.d₂₁_single, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, SheafOfModules.Presentation.IsFinite.finite_relations, Rep.freeLiftLEquiv_symm_apply, groupHomology.inhomogeneousChains.d_eq, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, CategoryTheory.ShortComplex.moduleCatMk_X₂_carrier, groupCohomology.coboundaries₂_ext_iff, groupHomology.d₁₀_comp_coinvariantsMk_assoc, MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, Rep.indToCoindAux_of_not_rel, groupCohomology.cocyclesOfIsCocycle₂_coe, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Rep.applyAsHom_hom, CoalgCat.toCoalgHom_id, forget_map, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupCohomology.H1π_comp_map, TopModuleCat.hom_comp, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, smulShortComplex_X₃_isModule, Rep.indResHomEquiv_apply_hom, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, CommRingCat.KaehlerDifferential.ext_iff, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, PresheafOfModules.germ_ringCat_smul, groupCohomology.cocyclesMk₀_eq, endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, groupHomology.single_mem_cycles₂_iff, groupCohomology.isoShortComplexH1_inv, groupHomology.boundaries₁_le_cycles₁, CoalgCat.toCoalgHom_comp, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, Rep.diagonalSuccIsoFree_hom_hom_single, CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, sMulCommClass_mk, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, QuadraticModuleCat.moduleCat_of_toModuleCat, PresheafOfModules.germ_smul, CoalgCat.leftUnitor_def, CoalgCat.of_counit, hom_neg, Rep.ihom_obj_ρ, instInvertibleCarrierOutModuleCatValSkeleton, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, Rep.free_ext_iff, PresheafOfModules.toSheafify_app_apply, MonoidalCategory.whiskerRight_def, isScalarTower_of_algebra_moduleCat, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, groupCohomology.cocycles₁_ext_iff, Algebra.instIsScalarTowerCarrier, groupCohomology.map_H0Iso_hom_f_assoc, ofHom_apply, TannakaDuality.FiniteGroup.ofRightFDRep_hom, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, simple_iff_isSimpleModule', restrictScalarsCongr_inv_app, groupCohomology.eq_d₁₂_comp_inv_assoc, Representation.linHom.invariantsEquivRepHom_apply_hom, groupCohomology.H1InfRes_f, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, TopModuleCat.hom_neg, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, instFreeCarrierX₂ModuleCatProjectiveShortComplex, forget₂AddCommGroupIsEquivalence, groupHomology.d₁₀ArrowIso_inv_left, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.single_mem_cycles₁_iff, Rep.coinvariantsFunctor_map_hom, groupHomology.d₂₁_single_ρ_add_single_inv_mul, HasLimit.productLimitCone_isLimit_lift, hom_injective, MonoidalCategory.tensorObj_carrier, Rep.linearization_map_hom_single, groupCohomology.isoShortComplexH2_inv, CategoryTheory.preadditiveCoyoneda_obj, groupCohomology.map_id_comp_H0Iso_hom_assoc, groupCohomology.isoCocycles₂_hom_comp_i_assoc, groupHomology.eq_d₁₀_comp_inv_apply, Rep.ihom_obj_V_carrier, LinearEquiv.toFGModuleCatIso_inv, ContinuousCohomology.const_app_hom, semilinearMapAddEquiv_apply, CoextendScalars.map'_hom_apply_apply, Rep.coindIso_hom_hom_hom, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, groupHomology.H0π_comp_H0Iso_hom_apply, Rep.barComplex.d_single, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, Rep.mono_iff_injective, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupHomology.d₂₁_comp_d₁₀_assoc, groupCohomology.coe_mapCocycles₂, groupCohomology.eq_d₀₁_comp_inv_assoc, isSimpleModule_of_simple, toKernelSubobject_arrow, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, CategoryTheory.Iso.toLinearMap_toLinearEquiv, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, groupCohomology.isoCocycles₁_hom_comp_i_assoc, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, groupHomology.mapCycles₁_quotientGroupMk'_epi, groupHomology.mapCycles₁_comp_i_assoc, groupHomology.H0π_comp_map_apply, restrictScalarsId'App_inv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, PresheafOfModules.Sheafify.SMulCandidate.h, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, groupHomology.π_comp_H2Iso_inv_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, groupCohomology.coboundariesOfIsCoboundary₂_coe, Rep.FiniteCyclicGroup.resolution.π_f, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, restrictScalarsComp'App_inv_apply, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mem_cycles₁_iff, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i, groupHomology.boundariesToCycles₁_apply, groupHomology.single_mem_cycles₂_iff_inv, groupHomology.d₁₀_single, TopModuleCat.hom_forget₂_TopCat_map, ihom_ev_app, groupCohomology.cocycles₁.d₁₂_apply, Rep.indResHomEquiv_symm_apply_hom, groupHomology.isoCycles₂_hom_comp_i_assoc, FilteredColimits.colimit_add_mk_eq, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, free_hom_ext_iff, CategoryTheory.Iso.toIsometryEquiv_symm, groupHomology.H2π_eq_zero_iff, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.Iso.toIsometryEquiv_trans, MonoidalCategory.associator_inv_apply, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, QuadraticModuleCat.hom_hom_associator, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.H1π_eq_iff, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, CoextendScalars.map_apply, groupHomology.chainsMap_f, Rep.quotientToCoinvariantsFunctor_obj_V, SheafOfModules.unitHomEquiv_apply_coe, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom, QuadraticModuleCat.hom_inv_associator, forget₂_map, groupCohomology.d₀₁_eq_zero, toMatrixModCat_obj_isModule
endRingEquiv 📖	CompOp	7 math math: FDRep.endRingEquiv_symm_comp_ρ, endRingEquiv_symm_apply_hom, Rep.Action_ρ_eq_ρ, FDRep.of_ρ, endRingEquiv_apply, Rep.ihom_obj_ρ, FDRep.endRingEquiv_comp_ρ
equivalenceSemimoduleCat 📖	CompOp	—
hasForgetToAddCommGroup 📖	CompOp	38 math math: HasColimit.colimitCocone_pt_isAddCommGroup, forget₂_reflectsLimitsOfSize, forget₂PreservesColimitsOfSize, forget₂AddCommGroup_preservesLimitsOfSize, forget₂_addCommGrp_essSurj, forget₂AddCommGroup_reflectsLimitOfShape, HasColimit.colimitCocone_ι_app, forget₂_addCommGroup_full, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, smul_naturality, HasColimit.colimitCocone_pt_isModule, CategoryTheory.preadditiveYoneda_obj, forget₂AddCommGroup_preservesLimits, forget₂_obj, CategoryTheory.whiskering_linearCoyoneda₂, smulNatTrans_apply_app, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, forget₂_obj_moduleCat_of, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, HasColimit.coconePointSMul_apply, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, mkOfSMul_smul, reflectsColimitsOfShape, forget₂AddCommGroup_reflectsLimitOfSize, HasColimit.colimitCocone_pt_carrier, forget₂_addCommGrp_additive, forget₂_reflectsLimits, forget₂PreservesColimitsOfShape, forget₂AddCommGroup_reflectsLimit, forget₂AddCommGroup_preservesLimit, CategoryTheory.whiskering_linearYoneda₂, HasColimit.reflectsColimit, forget₂AddCommGroupIsEquivalence, CategoryTheory.preadditiveCoyoneda_obj, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, forget₂_map
homAddEquiv 📖	CompOp	4 math math: homLinearEquiv_symm_apply, homAddEquiv_symm_apply_hom, homLinearEquiv_apply, homAddEquiv_apply
homEquiv 📖	CompOp	—
homLinearEquiv 📖	CompOp	5 math math: homLinearEquiv_symm_apply, Hom.hom₂_apply, homLinearEquiv_apply, monoidalClosed_pre_app, ihom_ev_app
homMk 📖	CompOp	3 math math: HasColimit.colimitCocone_ι_app, forget₂_map_homMk, homMk_hom_apply
instAddCommGroupCarrierMkOfSMul' 📖	CompOp	1 math math: HasColimit.colimitCocone_pt_isAddCommGroup
instAddCommGroupHom 📖	CompOp	10 math math: FGModuleCat.instFiniteHomModuleCatObjIsFG, homLinearEquiv_symm_apply, FGModuleCat.ihom_obj, hom_sum, Hom.hom₂_apply, homLinearEquiv_apply, ofHom₂_hom_apply_hom, ofHom₂_compr₂, monoidalClosed_pre_app, ihom_ev_app
instAddHom 📖	CompOp	9 math math: PresheafOfModules.add_app, homLinearEquiv_symm_apply, homAddEquiv_symm_apply_hom, hom_add, AlgebraicGeometry.tilde.map_add, homLinearEquiv_apply, homAddEquiv_apply, semilinearMapAddEquiv_symm_apply_apply, semilinearMapAddEquiv_apply
instCoeSortType 📖	CompOp	—
instConcreteCategoryLinearMapIdCarrier 📖	CompOp	427 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, instReflectsIsomorphismsForgetLinearMapIdCarrier, forget_preservesLimits, CommRingCat.KaehlerDifferential.map_d, MonoidalCategory.braiding_hom_apply, restrictScalars.map_apply, forget₂_reflectsLimitsOfSize, groupCohomology.isoCocycles₁_hom_comp_i_apply, forget_preservesLimitsOfSize, groupHomology.d₁₀_single_one, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, Rep.diagonalSuccIsoFree_inv_hom_single, Representation.repOfTprodIso_apply, freeHomEquiv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, forget₂AddCommGroup_preservesLimitsOfSize, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, LightCondensed.forget_obj_val_map, groupHomology.d₃₂_single, extendScalarsId_hom_app_one_tmul, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, ι_coprodIsoDirectSum_hom_apply, restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, LightCondensed.ihomPoints_symm_comp, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, AlternatingMap.postcomp_apply, linearIndependent_shortExact, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, monoidalClosed_uncurry, Rep.diagonalHomEquiv_symm_apply, CondensedMod.isDiscrete_tfae, groupCohomology.coe_mapCocycles₁, PresheafOfModules.pushforward_map_app_apply, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, PresheafOfModules.sections_property, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, QuadraticModuleCat.forget₂_map_associator_inv, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, groupCohomology.cocycles₂.d₂₃_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, groupHomology.isoCycles₁_inv_comp_iCycles_apply, forget₂_addCommGrp_essSurj, groupCohomology.map_H0Iso_hom_f_apply, groupCohomology.d₁₂_comp_d₂₃_apply, groupCohomology.H0IsoOfIsTrivial_inv_apply, PresheafOfModules.congr_map_apply, PresheafOfModules.freeYonedaEquiv_symm_app, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, PresheafOfModules.restrictScalarsObj_map, groupHomology.chains₁ToCoinvariantsKer_surjective, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MonoidalCategory.associator_hom_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, Rep.norm_comm_apply, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasColimit.colimitCocone_ι_app, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, forget₂_addCommGroup_full, PresheafOfModules.sectionsMap_coe, groupHomology.d₁₀_comp_coinvariantsMk_apply, Rep.diagonalSuccIsoFree_inv_hom_single_single, groupCohomology.H1IsoOfIsTrivial_inv_apply, PresheafOfModules.map_comp_apply, biprodIsoProd_inv_comp_snd_apply, PresheafOfModules.pushforward_map_app_apply', groupCohomology.H2π_comp_map_apply, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, HasColimit.colimitCocone_pt_isModule, CategoryTheory.preadditiveYoneda_obj, Rep.standardComplex.εToSingle₀_comp_eq, Rep.coindVEquiv_symm_apply_coe, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, imageIsoRange_inv_image_ι_apply, CondensedMod.isDiscrete_iff_isDiscrete_forget, PresheafOfModules.map_smul, FGModuleCat.FGModuleCatEvaluation_apply, epi_iff_surjective, PresheafOfModules.Monoidal.tensorObj_map_tmul, exteriorPower.map_mk, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, hom_inv_apply, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, monoidalClosed_curry, groupCohomology.d₀₁_apply_mem_cocycles₁, MonoidalCategory.leftUnitor_hom_apply, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.applyAsHom_comm_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, restrictScalarsId'App_hom_apply, groupCohomology.subtype_comp_d₀₁_apply, SheafOfModules.pushforwardComp_inv_app_val_app, FilteredColimits.forget_preservesFilteredColimits, groupCohomology.H2π_eq_iff, groupHomology.toCycles_comp_isoCycles₁_hom_apply, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, Rep.indToCoindAux_comm, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, groupHomology.cyclesIso₀_comp_H0π_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, CondensedMod.epi_iff_surjective_on_stonean, inv_hom_apply, forget₂AddCommGroup_preservesLimits, groupHomology.mapCycles₁_id_comp_apply, PresheafOfModules.presheaf_map_apply_coe, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, forget₂_obj, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, SheafOfModules.pushforwardCongr_hom_app_val_app, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, comp_apply, restrictScalarsCongr_hom_app, kernelIsoKer_inv_kernel_ι_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.whiskering_linearYoneda, MonoidalCategory.rightUnitor_hom_apply, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, FilteredColimits.M.mk_map, groupCohomology.π_comp_H0Iso_hom_apply, groupHomology.coe_mapCycles₂, CategoryTheory.whiskering_linearCoyoneda₂, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.H1π_comp_map_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MonoidalCategory.tensorLift_tmul, Rep.freeLiftLEquiv_apply, PresheafOfModules.surjective_of_epi, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, adj_homEquiv, LightCondensed.forget_map_val_app, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, piIsoPi_inv_kernel_ι_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Derivation.desc_d, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, groupCohomology.norm_ofAlgebraAutOnUnits_eq, PresheafOfModules.pushforward_obj_map_apply, groupHomology.d₂₁_comp_d₁₀_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, Rep.linearization_η_hom_apply, smulNatTrans_apply_app, forget_reflectsLimits, uliftFunctorForgetIso_inv_app, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, groupHomology.H1AddEquivOfIsTrivial_single, PresheafOfModules.unitHomEquiv_apply_coe, FreeMonoidal.εIso_inv_freeMk, groupHomology.isoCycles₂_hom_comp_i_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, SheafOfModules.pushforwardCongr_inv_app_val_app, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, free_η_freeMk, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, groupHomology.inhomogeneousChains.d_single, exteriorPower.iso₁_hom_apply, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, groupHomology.π_comp_H1Iso_hom_apply, groupCohomology.map_id_comp_H0Iso_hom_apply, forget_obj, PresheafOfModules.toPresheaf_map_app_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, ExtendScalars.map_tmul, FilteredColimits.forget_reflectsFilteredColimits, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, CategoryTheory.Iso.toLinearEquiv_apply, SheafOfModules.pushforwardComp_hom_app_val_app, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, MonoidalCategory.rightUnitor_inv_apply, groupCohomology.H1π_eq_zero_iff, Profinite.NobelingProof.GoodProducts.square_commutes, groupHomology.d₃₂_single_one_fst, Rep.coind'_ext_iff, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, PresheafOfModules.Elements.fromFreeYoneda_app_apply, HasColimit.coconePointSMul_apply, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, SheafOfModules.Presentation.mapRelations_mapGenerators, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, groupCohomology.cocyclesMk₁_eq, AlgCat.forget₂_module_obj, MonoidalCategory.leftUnitor_inv_apply, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, SheafOfModules.relationsOfIsCokernelFree_I, MonModuleEquivalenceAlgebra.algebraMap, MonoidalCategory.tensorμ_apply, groupHomology.d₂₁_apply_mem_cycles₁, ihom_map_apply, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.H2π_eq_zero_iff, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, groupCohomology.H1π_comp_map_apply, Rep.leftRegularHom_hom_single, CoalgCat.forget₂_obj, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, mkOfSMul_smul, kernelIsoKer_hom_ker_subtype_apply, groupHomology.cyclesMk₂_eq, groupHomology.H1π_eq_zero_iff, LightCondMod.hom_naturality_apply, groupHomology.d₂₁_single_one_fst, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, CoalgCat.forget₂_map, Rep.leftRegularHomEquiv_symm_single, groupCohomology.cocyclesMk₂_eq, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, groupHomology.cyclesMk₁_eq, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, LightCondensed.ihom_map_val_app, FreeMonoidal.μIso_inv_freeMk, groupCohomology.mapCocycles₁_comp_i_apply, groupHomology.mapCycles₂_id_comp_apply, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, Rep.hom_comm_apply, SheafOfModules.pushforwardNatTrans_app_val_app, groupHomology.H2π_comp_map_apply, HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, forget₂_addCommGrp_additive, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, groupHomology.d₂₁_single_one_snd, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, groupHomology.π_map_apply, groupHomology.d₃₂_single_one_snd, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, SheafOfModules.relationsOfIsCokernelFree_s, forget₂_reflectsLimits, forget₂PreservesColimitsOfShape, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, biproductIsoPi_inv_comp_π_apply, Rep.leftRegularHomEquiv_apply, PresheafOfModules.pushforward_obj_map_apply', forget₂AddCommGroup_reflectsLimit, groupHomology.coe_mapCycles₁, groupCohomology.d₀₁_comp_d₁₂_apply, free_map_apply, groupHomology.mapCycles₂_comp_i_apply, groupCohomology.cocyclesIso₀_hom_comp_f_apply, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.π_map_apply, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, PresheafOfModules.freeYonedaEquiv_comp, forget₂AddCommGroup_preservesLimit, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, FreeMonoidal.εIso_hom_one, Rep.freeLift_hom_single_single, groupHomology.π_comp_H1Iso_inv_apply, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.isoCocycles₂_hom_comp_i_apply, extendRestrictScalarsAdj_unit_app_apply, Rep.diagonalHomEquiv_apply, groupHomology.d₂₁_single, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, SheafOfModules.Presentation.IsFinite.finite_relations, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, MonoidalCategory.whiskerLeft_apply, groupHomology.cyclesMk₀_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, forget_map, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, span_rightExact, CommRingCat.KaehlerDifferential.ext_iff, groupCohomology.cocyclesMk₀_eq, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, MonoidalCategory.braiding_inv_apply, Rep.diagonalSuccIsoFree_hom_hom_single, Rep.free_ext_iff, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, ofHom_apply, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, restrictScalarsCongr_inv_app, imageIsoRange_hom_subtype_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, forget₂AddCommGroupIsEquivalence, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.d₂₁_single_ρ_add_single_inv_mul, Rep.linearization_map_hom_single, CategoryTheory.preadditiveCoyoneda_obj, groupHomology.eq_d₁₀_comp_inv_apply, LinearEquiv.toFGModuleCatIso_inv, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, groupHomology.H0π_comp_H0Iso_hom_apply, Rep.barComplex.d_single, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, Rep.mono_iff_injective, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupCohomology.coe_mapCocycles₂, toKernelSubobject_arrow, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, groupHomology.H0π_comp_map_apply, restrictScalarsId'App_inv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, groupHomology.π_comp_H2Iso_inv_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, restrictScalarsComp'App_inv_apply, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupHomology.d₁₀_single, groupCohomology.cocycles₁.d₁₂_apply, FilteredColimits.colimit_add_mk_eq, free_hom_ext_iff, groupHomology.H2π_eq_zero_iff, MonoidalCategory.associator_inv_apply, groupHomology.H1π_eq_iff, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, CoextendScalars.map_apply, SheafOfModules.unitHomEquiv_apply_coe, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, forget₂_map
instInhabited 📖	CompOp	—
instLinear 📖	CompOp	9 math math: Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, FGModuleCat.instFiniteHom, Rep.instLinearModuleCatCoinvariantsFunctor, Rep.instLinearModuleCatInvariantsFunctor, instMonoidalLinear, finite_ext, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, ofHom₂_compr₂, instLinearUliftFunctor
instModuleCarrierMkOfSMul' 📖	CompOp	1 math math: HasColimit.colimitCocone_pt_isModule
instNegHom 📖	CompOp	3 math math: PresheafOfModules.neg_app, AlgebraicGeometry.tilde.map_neg, hom_neg
instPreadditive 📖	CompOp	473 math math: groupHomology.mapShortComplexH2_τ₁, Rep.resCoindHomEquiv_symm_apply_hom, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Rep.resCoindHomEquiv_apply_hom, groupCohomology.mapShortComplexH1_τ₂, groupHomology.π_comp_H2Iso_hom_assoc, CategoryTheory.linearCoyoneda_obj_additive, biproductIsoPi_inv_comp_π, simple_of_finrank_eq_one, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom, CategoryTheory.additive_yonedaObj, groupCohomology.toCocycles_comp_isoCocycles₁_hom, Rep.MonoidalClosed.linearHomEquiv_symm_hom, groupCohomology.isoCocycles₁_hom_comp_i_apply, MoritaEquivalence.linear, cokernel_π_ext, groupHomology.mapShortComplexH2_id, groupHomology.shortComplexH1_f, groupCohomology.inhomogeneousCochains.d_def, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, groupCohomology.cocyclesIso₀_hom_comp_f, groupCohomology.eq_d₀₁_comp_inv, groupHomology.mapShortComplexH1_zero, FDRep.endRingEquiv_symm_comp_ρ, groupCohomology.π_comp_H1Iso_hom_assoc, groupHomology.mapShortComplexH2_zero, groupCohomology.eq_d₁₂_comp_inv, cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_carrier, groupCohomology.instPreservesZeroMorphismsRepCochainComplexModuleCatNatCochainsFunctor, groupCohomology.mapCocycles₂_comp_i, groupHomology.H1CoresCoinf_exact, groupHomology.eq_d₃₂_comp_inv, CategoryTheory.ShortComplex.moduleCatMk_X₁_isAddCommGroup, groupHomology.chainsMap_id, Rep.barComplex.d_def, Rep.diagonalHomEquiv_symm_apply, groupCohomology.H0IsoOfIsTrivial_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_g, groupHomology.comp_d₂₁_eq, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₂_isModule, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, groupHomology.H1CoresCoinf_X₃, groupCohomology.mapShortComplexH1_τ₃, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, groupCohomology.cochainsMap_comp, groupCohomology.comp_d₁₂_eq, groupHomology.π_comp_H1Iso_inv, CategoryTheory.ShortComplex.moduleCatMk_g, groupHomology.isoCycles₁_inv_comp_iCycles_apply, groupHomology.instPreservesZeroMorphismsRepModuleCatFunctor, groupCohomology.dArrowIso₀₁_inv_right, groupCohomology.map_H0Iso_hom_f_apply, shortExact_projectiveShortComplex, groupCohomology.eq_d₂₃_comp_inv_assoc, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, groupHomology.mapShortComplexH1_τ₂, Rep.standardComplex.d_eq, endRingEquiv_symm_apply_hom, groupHomology.H1CoresCoinfOfTrivial_X₁, groupHomology.chainsMap_id_f_map_mono, groupCohomology.mapShortComplexH2_comp_assoc, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, AlgebraicGeometry.instAdditiveModuleCatCarrierModulesSpecOfFunctor, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, instAdditiveLocalizationLocalizedModule_functor, groupCohomology.instMonoModuleCatFH1InfRes, smulShortComplex_X₃_isAddCommGroup, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.π_comp_H2Iso_inv_assoc, biprodIsoProd_inv_comp_snd_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃, groupHomology.eq_d₂₁_comp_inv, groupHomology.shortComplexH2_f, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, Profinite.NobelingProof.succ_exact, groupCohomology.dArrowIso₀₁_hom_right, Rep.MonoidalClosed.linearHomEquivComm_hom, CategoryTheory.ShortComplex.moduleCat_zero_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, groupHomology.mapCycles₁_comp_i, groupCohomology.shortComplexH0_f, groupCohomology.shortComplexH0_g, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, groupCohomology.shortComplexH1_f, Rep.standardComplex.εToSingle₀_comp_eq, groupHomology.inhomogeneousChains.d_def, Rep.coindVEquiv_symm_apply_coe, groupCohomology.comp_d₂₃_eq, cokernel_π_cokernelIsoRangeQuotient_hom, groupHomology.H1CoresCoinf_X₁, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₃_isAddCommGroup, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc, Module.Flat.iff_rTensor_preserves_shortComplex_exact, groupHomology.chainsMap_f_single, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, cokernel_π_imageSubobject_ext, groupCohomology.cochainsMap_f_map_epi, groupCohomology.comp_d₀₁_eq, LinearMap.shortExact_shortComplexKer, Module.Flat.iff_lTensor_preserves_shortComplex_exact, CategoryTheory.ShortComplex.moduleCatMk_X₃_carrier, groupHomology.mapCycles₂_comp_i, groupCohomology.map_H0Iso_hom_f, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, Rep.barResolution_complex, FGModuleCat.instFiniteHom, groupCohomology.cochainsMap_zero, smulShortComplex_X₁, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, groupCohomology.H1InfRes_X₂, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i, groupHomology.H1CoresCoinf_g, groupCohomology.cochainsMap_id_comp, smulShortComplex_g, groupCohomology.mapShortComplexH2_comp, groupCohomology.shortComplexH2_f, simple_iff_isSimpleModule, groupHomology.H1CoresCoinfOfTrivial_X₂, groupHomology.H1CoresCoinf_X₂, groupCohomology.cochainsMap_comp_assoc, groupHomology.π_comp_H2Iso_hom, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, groupHomology.mapCycles₁_comp_i_apply, groupHomology.chainsMap_f_map_epi, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, kernelIsoKer_inv_kernel_ι_apply, groupHomology.isoShortComplexH1_hom, groupCohomology.isoCocycles₂_hom_comp_i, Rep.resIndAdjunction_homEquiv_symm_apply, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, Rep.instLinearModuleCatCoinvariantsFunctor, Rep.coindMap'_hom, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₂, groupCohomology.dArrowIso₀₁_hom_left, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, groupCohomology.H1InfRes_X₃, simple_of_isSimpleModule, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, Rep.freeLiftLEquiv_apply, groupHomology.chainsFunctor_obj, groupCohomology.instMonoModuleCatFShortComplexH0, biprodIsoProd_inv_comp_snd, Rep.instPreservesZeroMorphismsModuleCatInvariantsFunctor, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, groupHomology.d₁₀ArrowIso_inv_right, range_mkQ_cokernelIsoRangeQuotient_inv, groupCohomology.mapShortComplexH2_zero, Rep.resIndAdjunction_homEquiv_apply, groupHomology.chainsMap_id_f_map_epi, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, groupCohomology.cochainsMap_id_f_map_mono, groupHomology.chainsMap_id_comp, Rep.leftRegularHomEquiv_symm_apply, groupHomology.instEpiModuleCatGH1CoresCoinf, groupCohomology.mapShortComplexH1_id, Rep.coinvariantsShortComplex_g, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, groupHomology.mapShortComplexH1_id_comp, groupHomology.mapShortComplexH1_comp, Rep.coindResAdjunction_homEquiv_apply, groupHomology.isoCycles₂_hom_comp_i_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, Rep.coinvariantsShortComplex_f, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles, groupHomology.eq_d₂₁_comp_inv_assoc, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom, smulShortComplex_X₃_carrier, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, CategoryTheory.preservesHomology_preadditiveCoyonedaObj_of_projective, Algebra.instLinearRestrictScalars, groupCohomology.mapShortComplexH2_τ₁, groupHomology.cyclesIso₀_inv_comp_iCycles, Representation.coind'_apply_apply, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, groupCohomology.mapShortComplexH2_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, Rep.coindIso_inv_hom_hom, groupHomology.mapShortComplexH2_comp, groupHomology.chainsMap_id_f_hom_eq_mapRange, groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, groupHomology.mapShortComplexH2_τ₂, groupHomology.chainsMap_f_map_mono, groupHomology.shortComplexH0_f, groupHomology.eq_d₁₀_comp_inv, FDRep.instHasKernels, groupHomology.isoShortComplexH1_inv, groupHomology.eq_d₁₀_comp_inv_assoc, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, groupHomology.isoCycles₁_hom_comp_i_apply, groupHomology.mapShortComplexH1_τ₁, hasCokernels_moduleCat, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, groupCohomology.cochainsMap_f, groupHomology.chainsMap_comp, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, Rep.instLinearModuleCatInvariantsFunctor, kernelIsoKer_hom_ker_subtype, smulShortComplex_f, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, groupCohomology.cocyclesMk₁_eq, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, groupCohomology.H1InfRes_X₁, groupHomology.shortComplexH0_exact, instAdditiveRestrictScalars, PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation, groupCohomology.mapCocycles₁_comp_i_assoc, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, instAdditiveUliftFunctor, groupHomology.eq_d₃₂_comp_inv_assoc, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, groupCohomology.π_comp_H2Iso_hom_assoc, groupCohomology.H1InfRes_g, CategoryTheory.preservesHomology_preadditiveYonedaObj_of_injective, Rep.standardComplex.d_comp_ε, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₃, FDRep.simple_iff_end_is_rank_one, CategoryTheory.linearYoneda_obj_additive, groupHomology.shortComplexH2_g, groupCohomology.mapShortComplexH1_id_comp, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, CategoryTheory.ShortComplex.moduleCat_exact_iff, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, groupCohomology.instPreservesZeroMorphismsRepModuleCatFunctor, groupHomology.isoShortComplexH2_hom, Rep.coindResAdjunction_homEquiv_symm_apply, kernelIsoKer_hom_ker_subtype_apply, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, Rep.coindVEquiv_apply_hom, groupCohomology.mapShortComplexH1_comp, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, groupHomology.π_comp_H1Iso_hom_assoc, groupHomology.chainsMap_f_2_comp_chainsIso₂, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_inv, groupCohomology.eq_d₂₃_comp_inv, instMonoidalLinear, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupCohomology.cochainsMap_f_map_mono, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_f, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, groupCohomology.isoShortComplexH1_hom, groupHomology.mapShortComplexH1_id, groupCohomology.isoCocycles₂_inv_comp_iCocycles, Rep.leftRegularHomEquiv_symm_single, restrictScalarsEquivalenceOfRingEquiv_additive, inhomogeneousCochains.d_eq, groupHomology.H1CoresCoinfOfTrivial_exact, MoritaEquivalence.instAdditiveModuleCatFunctorEqv, Rep.FiniteCyclicGroup.resolution_complex, groupHomology.chainsFunctor_map, groupCohomology.cocyclesMk₂_eq, groupHomology.instPreservesZeroMorphismsRepChainComplexModuleCatNatChainsFunctor, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, groupCohomology.cochainsMap_id_f_map_epi, groupHomology.chainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom, groupHomology.cyclesMk₁_eq, groupHomology.H1CoresCoinfOfTrivial_f, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, Rep.Action_ρ_eq_ρ, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, groupCohomology.H1InfRes_exact, groupCohomology.mapShortComplexH2_τ₂, groupCohomology.mapCocycles₁_comp_i_apply, ChainComplex.linearYonedaObj_d, Rep.standardComplex.instQuasiIsoNatεToSingle₀, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, Rep.standardComplex.x_projective, CategoryTheory.ShortComplex.moduleCatMk_X₁_isModule, groupCohomology.instAdditiveRepCochainComplexModuleCatNatCochainsFunctor, Rep.MonoidalClosed.linearHomEquiv_hom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, Rep.FiniteCyclicGroup.resolution_quasiIso, forget₂_addCommGrp_additive, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₁, groupHomology.H1CoresCoinfOfTrivial_g, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, groupCohomology.mapShortComplexH1_id_comp_assoc, groupCohomology.π_comp_H2Iso_hom_apply, groupCohomology.mapShortComplexH1_zero, IsSMulRegular.smulShortComplex_shortExact, CategoryTheory.ShortComplex.moduleCatMk_f, groupCohomology.mapShortComplexH1_comp_assoc, groupHomology.isoCycles₁_hom_comp_i_assoc, Rep.coinvariantsShortComplex_X₁, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, groupCohomology.isoShortComplexH2_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, groupCohomology.mapShortComplexH2_id_comp, CategoryTheory.ShortComplex.moduleCatMk_X₃_isModule, biprodIsoProd_inv_comp_fst, groupHomology.instEpiModuleCatGShortComplexH0, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, FDRep.of_ρ, biproductIsoPi_inv_comp_π_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, Rep.leftRegularHomEquiv_apply, groupHomology.isoCycles₁_inv_comp_iCycles, groupHomology.chainsMap_zero, groupHomology.H1CoresCoinfOfTrivial_g_epi, groupHomology.mapShortComplexH2_id_comp, groupHomology.isoShortComplexH2_inv, groupHomology.toCycles_comp_isoCycles₁_hom, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, groupHomology.mapCycles₂_comp_i_apply, groupCohomology.cocyclesIso₀_hom_comp_f_apply, groupCohomology.iCocycles_mk, groupHomology.isoCycles₂_hom_comp_i, groupHomology.π_comp_H1Iso_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, ofHom₂_compr₂, hasKernels_moduleCat, groupHomology.shortComplexH0_g, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, groupCohomology.mapShortComplexH2_id, groupHomology.d₁₀ArrowIso_hom_right, groupCohomology.shortComplexH0_exact, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, groupHomology.π_comp_H1Iso_inv_apply, groupCohomology.isoCocycles₂_hom_comp_i_apply, instMonoidalPreadditive, groupHomology.H1CoresCoinfOfTrivial_X₃, Rep.diagonalHomEquiv_apply, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, Rep.freeLiftLEquiv_symm_apply, groupHomology.inhomogeneousChains.d_eq, groupHomology.eq_d₂₁_comp_inv_apply, CategoryTheory.ShortComplex.moduleCatMk_X₂_carrier, groupCohomology.cochainsFunctor_map, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, groupCohomology.shortComplexH2_g, Rep.coinvariantsShortComplex_X₂, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, smulShortComplex_X₃_isModule, Rep.indResHomEquiv_apply_hom, groupHomology.mapShortComplexH1_τ₃, instLinearUliftFunctor, groupCohomology.cocyclesMk₀_eq, endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, groupCohomology.isoShortComplexH1_inv, CategoryTheory.additive_coyonedaObj, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, groupHomology.H1CoresCoinf_f, Rep.ihom_obj_ρ, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, groupCohomology.cochainsMap_id_comp_assoc, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, groupCohomology.map_H0Iso_hom_f_assoc, CategoryTheory.ShortComplex.Exact.moduleCat_of_range_eq_ker, kernelIsoKer_inv_kernel_ι, simple_iff_isSimpleModule', groupHomology.shortComplexH1_g, Rep.instPreservesZeroMorphismsModuleCatCoinvariantsFunctor, groupCohomology.eq_d₁₂_comp_inv_assoc, Representation.linHom.invariantsEquivRepHom_apply_hom, groupCohomology.H1InfRes_f, Rep.instAdditiveModuleCatInvariantsFunctor, smulShortComplex_X₂, instFreeCarrierX₂ModuleCatProjectiveShortComplex, Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eq, groupHomology.d₁₀ArrowIso_inv_left, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π, groupCohomology.mapShortComplexH2_τ₃, groupCohomology.isoShortComplexH2_inv, Algebra.restrictScalarsEquivalenceOfRingEquiv_linear, groupCohomology.isoCocycles₂_hom_comp_i_assoc, groupHomology.eq_d₁₀_comp_inv_apply, Rep.coinvariantsShortComplex_X₃, Rep.coindIso_hom_hom_hom, groupHomology.mapShortComplexH2_τ₃, groupCohomology.eq_d₀₁_comp_inv_assoc, toKernelSubobject_arrow, instHasBinaryBiproducts, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, smulShortComplex_g_epi, groupCohomology.isoCocycles₁_hom_comp_i_assoc, Rep.coinvariantsShortComplex_shortExact, groupHomology.π_comp_H1Iso_inv_assoc, Rep.FiniteCyclicGroup.resolution_π, groupHomology.mapCycles₁_comp_i_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc, groupCohomology.mapShortComplexH1_τ₁, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, smulShortComplex_exact, groupHomology.π_comp_H2Iso_inv_apply, Rep.FiniteCyclicGroup.resolution.π_f, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, Rep.instAdditiveModuleCatCoinvariantsFunctor, groupCohomology.cochainsFunctor_obj, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i, FDRep.simple_iff_char_is_norm_one, Rep.indResHomEquiv_symm_apply_hom, groupHomology.isoCycles₂_hom_comp_i_assoc, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, groupHomology.chainsMap_f_0_comp_chainsIso₀, CategoryTheory.ShortComplex.moduleCatMk_X₂_isAddCommGroup, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, instHasFiniteBiproducts, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, biprodIsoProd_inv_comp_fst_apply, FGModuleCat.instIsIsoCoimageImageComparison, groupCohomology.shortComplexH1_g, groupHomology.chainsMap_f, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, groupCohomology.cochainsMap_id, ChainComplex.linearYonedaObj_X
instSMulCarrierMkOfSMul' 📖	CompOp	1 math math: mkOfSMul'_smul
instSMulHom 📖	CompOp	1 math math: hom_smul
instSMulIntHom 📖	CompOp	2 math math: PresheafOfModules.zsmul_app, hom_zsmul
instSMulNatHom 📖	CompOp	1 math math: hom_nsmul
instSubHom 📖	CompOp	3 math math: AlgebraicGeometry.tilde.map_sub, PresheafOfModules.sub_app, hom_sub
instZeroHom 📖	CompOp	22 math math: hom_zero, groupHomology.map₁_one, groupCohomology.d₀₁_comp_d₁₂, groupHomology.d₃₂_comp_d₂₁_assoc, groupCohomology.map₁_one, groupCohomology.mapCocycles₁_one, groupHomology.d₁₀_comp_coinvariantsMk, groupCohomology.inhomogeneousCochains.d_comp_d, groupCohomology.d₁₂_comp_d₂₃_assoc, groupCohomology.subtype_comp_d₀₁_assoc, groupCohomology.d₁₂_comp_d₂₃, groupHomology.d₂₁_comp_d₁₀, groupHomology.inhomogeneousChains.d_comp_d, groupHomology.d₁₀_eq_zero_of_isTrivial, groupCohomology.d₀₁_comp_d₁₂_assoc, AlgebraicGeometry.tilde.map_zero, groupHomology.d₃₂_comp_d₂₁, groupCohomology.subtype_comp_d₀₁, groupHomology.d₁₀_comp_coinvariantsMk_assoc, groupHomology.d₂₁_comp_d₁₀_assoc, PresheafOfModules.zero_app, groupCohomology.d₀₁_eq_zero
isAddCommGroup 📖	CompOp	822 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, Rep.resCoindHomEquiv_symm_apply_hom, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, Rep.resCoindHomEquiv_apply_hom, hom_zero, instReflectsIsomorphismsForgetLinearMapIdCarrier, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective, of_coe, forget_preservesLimits, TopModuleCat.hom_zero, CommRingCat.KaehlerDifferential.map_d, MonoidalCategory.braiding_hom_apply, biproductIsoPi_inv_comp_π, FilteredColimits.colimit_smul_mk_eq, restrictScalars.map_apply, forget₂_reflectsLimitsOfSize, Rep.MonoidalClosed.linearHomEquiv_symm_hom, groupCohomology.isoCocycles₁_hom_comp_i_apply, ContinuousCohomology.I_obj_V_isAddCommGroup, groupHomology.coinfNatTrans_app, CategoryTheory.Iso.toCoalgEquiv_symm, forget_preservesLimitsOfSize, LinearMap.id_fgModuleCat_comp, groupHomology.d₁₀_single_one, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, FGModuleCat.hom_hom_id, Rep.diagonalSuccIsoFree_inv_hom_single, Representation.repOfTprodIso_apply, freeHomEquiv_apply, epi_as_hom''_mkQ, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, forget₂AddCommGroup_preservesLimitsOfSize, toMatrixModCat_map, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, LightCondensed.forget_obj_val_map, groupCohomology.cocyclesIso₀_hom_comp_f, Rep.resCoindAdjunction_counit_app_hom_hom, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, groupHomology.d₃₂_single, TopModuleCat.hom_zero_apply, Rep.coindToInd_of_support_subset_orbit, extendScalarsId_hom_app_one_tmul, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, groupCohomology.π_comp_H0Iso_hom, FDRep.endRingEquiv_symm_comp_ρ, ι_coprodIsoDirectSum_hom_apply, restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, LightCondensed.ihomPoints_symm_comp, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, AlternatingMap.postcomp_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_isAddCommGroup, QuadraticModuleCat.toIsometry_comp, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, monoidalClosed_uncurry, Rep.diagonalHomEquiv_symm_apply, groupCohomology.H0IsoOfIsTrivial_hom, CondensedMod.isDiscrete_tfae, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, Iso.homCongr_eq_arrowCongr, CoextendScalars.smul_apply', groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, PresheafOfModules.pushforward_map_app_apply, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, PresheafOfModules.sections_property, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, PresheafOfModules.toSheafify_app_apply', PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, Rep.coinvariantsAdjunction_counit_app, forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, QuadraticModuleCat.forget₂_map_associator_inv, LinearMap.comp_id_fgModuleCat, RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, toMatrixModCat_obj_isAddCommGroup, groupCohomology.cocycles₂.d₂₃_apply, groupCohomology.d₀₁_hom_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, hom_surjective, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CoalgCat.tensorObj_isAddCommGroup, forget₂_addCommGrp_essSurj, groupCohomology.map_H0Iso_hom_f_apply, groupCohomology.d₁₂_comp_d₂₃_apply, groupCohomology.H0IsoOfIsTrivial_inv_apply, PresheafOfModules.congr_map_apply, PresheafOfModules.freeYonedaEquiv_symm_app, Rep.finsuppToCoinvariantsTensorFree_single, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, PresheafOfModules.restrictScalarsObj_map, groupHomology.chains₁ToCoinvariantsKer_surjective, Rep.coinvariantsTensorFreeLEquiv_symm_apply, TopModuleCat.continuousSMul, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Rep.resCoindAdjunction_unit_app_hom_hom, endRingEquiv_symm_apply_hom, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, Rep.homEquiv_apply_hom, FilteredColimits.colimit_zero_eq, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MonoidalCategory.associator_hom_apply, CategoryTheory.Iso.toCoalgEquiv_toCoalgHom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, Rep.norm_comm_apply, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasLimit.productLimitCone_cone_π, HasColimit.colimitCocone_ι_app, CoalgCat.moduleCat_of_toModuleCat, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, PresheafOfModules.Derivation.postcomp_d_apply, smulShortComplex_X₃_isAddCommGroup, forget₂_addCommGroup_full, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, PresheafOfModules.Derivation.d_one, PresheafOfModules.sectionsMap_coe, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.diagonalSuccIsoFree_inv_hom_single_single, groupCohomology.H1IsoOfIsTrivial_inv_apply, PresheafOfModules.Sheafify.map_smul_eq, PresheafOfModules.map_comp_apply, biprodIsoProd_inv_comp_snd_apply, RestrictionCoextensionAdj.counit'_app, PresheafOfModules.pushforward_map_app_apply', PresheafOfModules.Derivation.d_mul, isFG_iff, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Rep.ihom_ev_app_hom, homLinearEquiv_symm_apply, hom_smul, uliftFunctorForgetIso_hom_app, Rep.MonoidalClosed.linearHomEquivComm_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, FGModuleCat.hom_comp, ContinuousCohomology.I_obj_ρ_apply, imageIsoRange_hom_subtype, GradedObject.finrankSupport_subset_iff, CategoryTheory.Iso.toIsometryEquiv_toFun, CoextendScalars.smul_apply, groupCohomology.shortComplexH0_f, binaryProductLimitCone_cone_π_app_right, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, HasColimit.colimitCocone_pt_isModule, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.linearCoyoneda_obj_obj_isAddCommGroup, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, Rep.subtype_hom, Rep.coindVEquiv_symm_apply_coe, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, imageIsoRange_inv_image_ι_apply, CategoryTheory.preadditiveYonedaMap_app, CondensedMod.isDiscrete_iff_isDiscrete_forget, PresheafOfModules.map_smul, FGModuleCat.FGModuleCatEvaluation_apply, epi_iff_surjective, PresheafOfModules.Monoidal.tensorObj_map_tmul, exteriorPower.map_mk, TopModuleCat.ofHom_hom, cokernel_π_cokernelIsoRangeQuotient_hom, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, hom_inv_apply, CategoryTheory.ShortComplex.moduleCatMk_X₃_isAddCommGroup, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, monoidalClosed_curry, groupCohomology.d₀₁_apply_mem_cocycles₁, QuadraticModuleCat.instMonoidalCategory.tensorObj_form, CoalgCat.tensorHom_def, Module.Flat.iff_rTensor_preserves_shortComplex_exact, MonoidalCategory.leftUnitor_hom_apply, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.coinvariantsFunctor_obj_carrier, Rep.applyAsHom_comm_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, restrictScalarsId'App_hom_apply, groupCohomology.subtype_comp_d₀₁_apply, ContinuousCohomology.Iobj_ρ_apply, SheafOfModules.pushforwardComp_inv_app_val_app, FilteredColimits.forget_preservesFilteredColimits, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, homAddEquiv_symm_apply_hom, Rep.coinvariantsTensorFreeLEquiv_apply, PresheafOfModules.pushforward₀_obj_obj_isAddCommGroup, groupHomology.toCycles_comp_isoCycles₁_hom_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, localizedModule_isLocalizedModule, range_eq_top_of_epi, groupCohomology.map_H0Iso_hom_f, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, Derivation.d_mul, Rep.indToCoindAux_comm, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, ContinuousCohomology.I_obj_V_isModule, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, groupHomology.cyclesIso₀_comp_H0π_apply, CoalgCat.associator_def, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, CondensedMod.epi_iff_surjective_on_stonean, hom_whiskerRight, hom_inv_associator, FGModuleCat.hom_id, lof_coprodIsoDirectSum_inv, TopModuleCat.hom_add, BialgCat.forget₂_coalgebra_obj, CoalgCat.MonoidalCategoryAux.tensorObj_comul, CoalgCat.comul_def, inv_hom_apply, forget₂AddCommGroup_preservesLimits, directLimitIsColimit_desc, groupHomology.mapCycles₁_id_comp_apply, MonoidalCategory.rightUnitor_def, CategoryTheory.Iso.toLinearEquiv_symm, PresheafOfModules.presheaf_map_apply_coe, smulShortComplex_g, directLimitCocone_pt_isAddCommGroup, CategoryTheory.linearYoneda_obj_obj_isAddCommGroup, PresheafOfModules.Derivation.congr_d, MonoidalCategory.associator_def, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, forget₂_obj, Rep.indResAdjunction_counit_app_hom_hom, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Rep.coindToInd_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, SheafOfModules.pushforwardCongr_hom_app_val_app, hom_whiskerLeft, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, comp_apply, restrictScalarsCongr_hom_app, kernelIsoKer_inv_kernel_ι_apply, ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.whiskering_linearYoneda, MonoidalCategory.rightUnitor_hom_apply, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CoalgCat.whiskerRight_def, TopModuleCat.hom_zsmul, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, FilteredColimits.M.mk_map, groupCohomology.π_comp_H0Iso_hom_apply, groupHomology.coe_mapCycles₂, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, CategoryTheory.whiskering_linearCoyoneda₂, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.H1π_comp_map_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MatrixModCat.toModuleCat_obj_carrier, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, Rep.freeLiftLEquiv_apply, hom_hom_leftUnitor, PresheafOfModules.surjective_of_epi, adj_homEquiv, instIsScalarTowerLocalizationCarrierLocalizedModule, hom_hom_rightUnitor, LightCondensed.forget_map_val_app, biprodIsoProd_inv_comp_snd, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, CategoryTheory.Iso.toCoalgEquiv_refl, piIsoPi_inv_kernel_ι_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, ker_eq_bot_of_mono, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, Rep.finsuppTensorRight_hom_hom, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, groupCohomology.norm_ofAlgebraAutOnUnits_eq, groupCohomology.π_comp_H0Iso_hom_assoc, imageIsoRange_hom_subtype_assoc, QuadraticModuleCat.toIsometry_whiskerRight, PresheafOfModules.pushforward_obj_map_apply, groupHomology.d₂₁_comp_d₁₀_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CoalgCat.forget_reflects_isos, groupCohomology.d₀₁_ker_eq_invariants, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, Rep.linearization_η_hom_apply, smulNatTrans_apply_app, FGModuleCat.ihom_obj, TopModuleCat.hom_id, forget_reflectsLimits, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, CoalgCat.tensorUnit_isAddCommGroup, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, groupHomology.H1AddEquivOfIsTrivial_single, CoalgCat.ofComonObjCoalgebraStruct_comul, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, groupHomology.range_d₁₀_eq_coinvariantsKer, QuadraticModuleCat.toIsometry_tensorHom, PresheafOfModules.unitHomEquiv_apply_coe, FreeMonoidal.εIso_inv_freeMk, groupHomology.isoCycles₂_hom_comp_i_apply, Rep.ofModuleMonoidAlgebra_obj_ρ, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, QuadraticModuleCat.toIsometry_hom_leftUnitor, Rep.coinvariantsShortComplex_f, SheafOfModules.pushforwardCongr_inv_app_val_app, QuadraticModuleCat.toIsometry_hom_rightUnitor, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, RestrictionCoextensionAdj.unit'_app, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierOfCarrierStalkAbPresheafPrimeComplAsIdealHomToStalk, imageIsoRange_inv_image_ι, smulShortComplex_X₃_carrier, free_η_freeMk, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, ContinuousCohomology.I_map_hom, groupHomology.inhomogeneousChains.d_single, exteriorPower.iso₁_hom_apply, TopModuleCat.freeMap_map, QuadraticModuleCat.Hom.toIsometry_injective, CoalgCat.Hom.toCoalgHom_injective, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, hom_inv_rightUnitor, ExtendScalars.smul_tmul, hom_sum, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, CategoryTheory.Iso.toCoalgEquiv_trans, groupHomology.π_comp_H1Iso_hom_apply, hom_nsmul, groupCohomology.map_id_comp_H0Iso_hom_apply, forget_obj, directLimitDiagram_obj_isAddCommGroup, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.chainsMap_id_f_hom_eq_mapRange, PresheafOfModules.toPresheaf_map_app_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupCohomology.map_id_comp_H0Iso_hom, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, PresheafOfModules.Derivation'.d_app, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, CategoryTheory.Iso.toIsometryEquiv_refl, QuadraticModuleCat.toIsometry_inv_rightUnitor, ExtendScalars.map_tmul, FilteredColimits.colimit_add_mk_eq', QuadraticModuleCat.cliffordAlgebra_map, FilteredColimits.forget_reflectsFilteredColimits, LinearMap.id_moduleCat_comp, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, QuadraticModuleCat.toIsometry_whiskerLeft, CategoryTheory.Iso.toLinearEquiv_apply, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, Derivation.d_map, SheafOfModules.pushforwardComp_hom_app_val_app, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, Rep.toCoinvariantsMkQ_hom, MonoidalCategory.tensorObj, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, imageIsoRange_inv_image_ι_assoc, MonoidalCategory.rightUnitor_inv_apply, groupCohomology.H1π_eq_zero_iff, groupHomology.H1AddEquivOfIsTrivial_symm_apply, Rep.invariantsAdjunction_counit_app_hom, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, groupHomology.d₃₂_single_one_fst, CoalgCat.MonoidalCategoryAux.counit_tensorObj, Rep.coind'_ext_iff, CoalgCat.counit_def, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, PresheafOfModules.Elements.fromFreeYoneda_app_apply, binaryProductLimitCone_cone_π_app_left, HasColimit.coconePointSMul_apply, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, kernelIsoKer_hom_ker_subtype, smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, hom_add, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, groupCohomology.cocyclesMk₁_eq, AlgCat.forget₂_module_obj, MonoidalCategory.leftUnitor_inv_apply, ι_coprodIsoDirectSum_hom, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, SheafOfModules.relationsOfIsCokernelFree_I, MonModuleEquivalenceAlgebra.algebraMap, MonoidalCategory.tensorμ_apply, Rep.quotientToInvariantsFunctor_obj_V, MonoidalCategory.tensorObj_isModule, MonoidalCategory.tensorObj_isAddCommGroup, groupHomology.d₂₁_apply_mem_cycles₁, ihom_map_apply, MonModuleEquivalenceAlgebra.inverseObj_mul, ihom_coev_app, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.H2π_eq_zero_iff, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, TopModuleCat.isTopologicalAddGroup, groupCohomology.H1π_comp_map_apply, free_shortExact, Rep.leftRegularHom_hom_single, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, hom_hom_associator, CoalgCat.forget₂_obj, Rep.finsuppTensorRight_inv_hom, Rep.coinvariantsMk_app_hom, Rep.ihom_obj_V_isAddCommGroup, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, CategoryTheory.ShortComplex.moduleCat_exact_iff, groupHomology.mapCycles₂_hom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, mkOfSMul_smul, MatrixModCat.isScalarTower_toModuleCat, restrictScalars.smul_def, CoalgCat.whiskerLeft_def, TopModuleCat.hom_sub, kernelIsoKer_hom_ker_subtype_apply, CategoryTheory.preadditiveYonedaObj_obj_isAddCommGroup, QuadraticModuleCat.toIsometry_id, groupHomology.cyclesMk₂_eq, Rep.coindVEquiv_apply_hom, PresheafOfModules.Derivation.d_app, groupHomology.H1π_eq_zero_iff, LightCondMod.hom_naturality_apply, TopModuleCat.forget₂_TopCat_obj, groupHomology.d₂₁_single_one_fst, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, HasLimit.productLimitCone_cone_pt_isModule, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, TopModuleCat.hom_nsmul, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, Derivation.d_add, Rep.ihom_map_hom, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, groupHomology.H1AddEquivOfIsTrivial_apply, MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, Rep.finsuppTensorLeft_inv_hom, TopModuleCat.instIsTopologicalAddGroupCarrier, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, PresheafOfModules.Derivation'.app_apply, CoalgCat.forget₂_map, Rep.leftRegularHomEquiv_symm_single, piIsoPi_hom_ker_subtype, hom_id, groupCohomology.cocyclesMk₂_eq, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.chainsMap_f_hom, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, piIsoPi_inv_kernel_ι, Rep.norm_hom, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.indResAdjunction_unit_app_hom_hom, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, groupHomology.cyclesMk₁_eq, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, LightCondensed.ihom_map_val_app, TopModuleCat.cokerπ_surjective, FreeMonoidal.μIso_inv_freeMk, uliftFunctor_map, Rep.Action_ρ_eq_ρ, MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, ofHom_hom, Rep.coindMap_hom, groupHomology.mapCycles₂_id_comp_apply, instFiniteCarrierObjModuleCatIsFG, Rep.MonoidalClosed.linearHomEquiv_hom, Rep.invariantsAdjunction_homEquiv_apply_hom, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, localizedModuleMap_hom_apply, Rep.hom_comm_apply, SheafOfModules.pushforwardNatTrans_app_val_app, groupHomology.H2π_comp_map_apply, Hom.hom₂_apply, CategoryTheory.Iso.toIsometryEquiv_invFun, TopModuleCat.hom_smul, HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, uliftFunctor_obj, forget₂_addCommGrp_additive, Module.Flat.iff_preservesFiniteLimits_tensorLeft, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, CoalgCat.MonoidalCategoryAux.comul_tensorObj, Rep.finsuppTensorLeft_hom_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, projective_of_module_projective, MatrixModCat.toModuleCat_map, MonoidalCategory.leftUnitor_def, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, binaryProductLimitCone_isLimit_lift, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, homLinearEquiv_apply, Rep.coinvariantsTensorMk_apply, TopModuleCat.kerι_apply, Rep.indMap_hom, Rep.homEquiv_symm_apply_hom, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Rep.invariantsFunctor_map_hom, Iso.conj_eq_conj, CoalgCat.toComon_map_hom, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, MonoidalCategory.tensorObj_def, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, groupHomology.d₂₁_single_one_snd, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, biprodIsoProd_inv_comp_fst, groupHomology.π_map_apply, CoalgCat.rightUnitor_def, BialgCat.forget₂_coalgebra_map, groupHomology.d₃₂_single_one_snd, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, QuadraticModuleCat.cliffordAlgebra_obj_carrier, groupHomology.π_comp_H2Iso_hom_apply, CoalgCat.tensorObj_carrier, SheafOfModules.relationsOfIsCokernelFree_s, forget₂_reflectsLimits, FDRep.of_ρ, forget₂PreservesColimitsOfShape, MatrixModCat.toModuleCat_obj_isAddCommGroup, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, Rep.ihom_coev_app_hom, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, Rep.leftRegularHomEquiv_apply, restrictScalars.smul_def', PresheafOfModules.pushforward_obj_map_apply', free_shortExact_rank_add, FGModuleCat.FGModuleCatEvaluation_apply', forget₂AddCommGroup_reflectsLimit, groupHomology.coe_mapCycles₁, HasLimit.productLimitCone_cone_pt_isAddCommGroup, hom_inv_leftUnitor, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, groupCohomology.d₀₁_comp_d₁₂_apply, free_map_apply, groupHomology.mapCycles₂_comp_i_apply, binaryProductLimitCone_cone_pt, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ofHom₂_hom_apply_hom, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, groupCohomology.subtype_comp_d₀₁, Rep.freeLift_hom, CoalgCat.tensorObj_instCoalgebra, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.π_map_apply, hom_sub, CoalgCat.ofComonObjCoalgebraStruct_counit, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, ofHom₂_compr₂, Algebra.instSMulCommClassCarrier, PresheafOfModules.freeYonedaEquiv_comp, forget₂AddCommGroup_preservesLimit, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, CoalgCat.tensorObj_isModule, FreeMonoidal.εIso_hom_one, QuadraticModuleCat.toIsometry_inv_leftUnitor, Rep.freeLift_hom_single_single, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, mono_iff_ker_eq_bot, groupHomology.π_comp_H1Iso_inv_apply, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.isoCocycles₂_hom_comp_i_apply, extendRestrictScalarsAdj_unit_app_apply, hom_bijective, Rep.diagonalHomEquiv_apply, groupHomology.d₂₁_single, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, SheafOfModules.Presentation.IsFinite.finite_relations, groupHomology.inhomogeneousChains.d_eq, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, groupHomology.cyclesMk₀_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Rep.applyAsHom_hom, CoalgCat.toCoalgHom_id, forget_map, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, TopModuleCat.hom_comp, smulShortComplex_X₃_isModule, Rep.indResHomEquiv_apply_hom, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, CommRingCat.KaehlerDifferential.ext_iff, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, PresheafOfModules.germ_ringCat_smul, groupCohomology.cocyclesMk₀_eq, endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, CoalgCat.toCoalgHom_comp, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, Rep.diagonalSuccIsoFree_hom_hom_single, CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, sMulCommClass_mk, QuadraticModuleCat.moduleCat_of_toModuleCat, PresheafOfModules.germ_smul, CoalgCat.leftUnitor_def, hom_neg, Rep.ihom_obj_ρ, instInvertibleCarrierOutModuleCatValSkeleton, Rep.free_ext_iff, PresheafOfModules.toSheafify_app_apply, MonoidalCategory.whiskerRight_def, isScalarTower_of_algebra_moduleCat, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, Algebra.instIsScalarTowerCarrier, groupCohomology.map_H0Iso_hom_f_assoc, ofHom_apply, TannakaDuality.FiniteGroup.ofRightFDRep_hom, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, simple_iff_isSimpleModule', restrictScalarsCongr_inv_app, Representation.linHom.invariantsEquivRepHom_apply_hom, Rep.mkQ_hom, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, TopModuleCat.hom_neg, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, forget₂AddCommGroupIsEquivalence, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, Rep.coinvariantsFunctor_map_hom, groupHomology.d₂₁_single_ρ_add_single_inv_mul, HasLimit.productLimitCone_isLimit_lift, hom_injective, MonoidalCategory.tensorObj_carrier, Rep.linearization_map_hom_single, CategoryTheory.preadditiveCoyoneda_obj, groupCohomology.map_id_comp_H0Iso_hom_assoc, groupHomology.eq_d₁₀_comp_inv_apply, LinearEquiv.toFGModuleCatIso_inv, ContinuousCohomology.const_app_hom, semilinearMapAddEquiv_apply, CoextendScalars.map'_hom_apply_apply, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, PresheafOfModules.ofPresheaf_obj_isAddCommGroup, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, groupHomology.H0π_comp_H0Iso_hom_apply, Rep.barComplex.d_single, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, Rep.mono_iff_injective, MonoidalCategory.tensorUnit_isAddCommGroup, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupCohomology.coe_mapCocycles₂, isSimpleModule_of_simple, toKernelSubobject_arrow, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, CategoryTheory.Iso.toLinearMap_toLinearEquiv, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, groupHomology.H0π_comp_map_apply, restrictScalarsId'App_inv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, PresheafOfModules.Sheafify.SMulCandidate.h, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, groupHomology.π_comp_H2Iso_inv_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, restrictScalarsComp'App_inv_apply, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupHomology.d₁₀_single, TopModuleCat.hom_forget₂_TopCat_map, ihom_ev_app, groupCohomology.cocycles₁.d₁₂_apply, Rep.indResHomEquiv_symm_apply_hom, FilteredColimits.colimit_add_mk_eq, free_hom_ext_iff, CategoryTheory.Iso.toIsometryEquiv_symm, groupHomology.H2π_eq_zero_iff, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.ShortComplex.moduleCatMk_X₂_isAddCommGroup, CategoryTheory.Iso.toIsometryEquiv_trans, MonoidalCategory.associator_inv_apply, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, QuadraticModuleCat.hom_hom_associator, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.H1π_eq_iff, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, CoextendScalars.map_apply, groupHomology.chainsMap_f, Rep.quotientToCoinvariantsFunctor_obj_V, SheafOfModules.unitHomEquiv_apply_coe, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, QuadraticModuleCat.hom_inv_associator, forget₂_map, toMatrixModCat_obj_isModule
isModule 📖	CompOp	1017 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, Rep.resCoindHomEquiv_symm_apply_hom, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, Rep.resCoindHomEquiv_apply_hom, groupCohomology.instEpiModuleCatH2π, hom_zero, groupHomology.π_comp_H2Iso_hom_assoc, instReflectsIsomorphismsForgetLinearMapIdCarrier, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, PresheafOfModules.Sheafify.app_eq_of_isLocallyInjective, of_coe, forget_preservesLimits, TopModuleCat.hom_zero, directLimitDiagram_obj_isModule, CommRingCat.KaehlerDifferential.map_d, MonoidalCategory.braiding_hom_apply, biproductIsoPi_inv_comp_π, FilteredColimits.colimit_smul_mk_eq, groupHomology.mapCycles₂_comp_assoc, restrictScalars.map_apply, forget₂_reflectsLimitsOfSize, groupCohomology.toCocycles_comp_isoCocycles₁_hom, Rep.MonoidalClosed.linearHomEquiv_symm_hom, groupCohomology.isoCocycles₁_hom_comp_i_apply, PresheafOfModules.ofPresheaf_obj_isModule, groupCohomology.mem_cocycles₂_def, groupHomology.coinfNatTrans_app, CategoryTheory.Iso.toCoalgEquiv_symm, forget_preservesLimitsOfSize, groupCohomology.d₂₃_hom_apply, LinearMap.id_fgModuleCat_comp, groupHomology.d₁₀_single_one, groupHomology.boundaries₂_le_cycles₂, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, FGModuleCat.hom_hom_id, Rep.diagonalSuccIsoFree_inv_hom_single, groupCohomology.d₀₁_comp_d₁₂, Representation.repOfTprodIso_apply, freeHomEquiv_apply, epi_as_hom''_mkQ, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, forget₂AddCommGroup_preservesLimitsOfSize, toMatrixModCat_map, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, LightCondensed.forget_obj_val_map, groupCohomology.cocyclesIso₀_hom_comp_f, Rep.resCoindAdjunction_counit_app_hom_hom, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, groupHomology.d₃₂_single, TopModuleCat.hom_zero_apply, groupCohomology.eq_d₀₁_comp_inv, extendScalarsId_hom_app_one_tmul, groupCohomology.H1π_comp_map_assoc, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, groupCohomology.π_comp_H0Iso_hom, FDRep.endRingEquiv_symm_comp_ρ, groupCohomology.π_comp_H1Iso_hom_assoc, ι_coprodIsoDirectSum_hom_apply, restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, LightCondensed.ihomPoints_symm_comp, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, Rep.indToCoindAux_self, groupCohomology.mapCocycles₂_comp_i, AlternatingMap.postcomp_apply, groupHomology.eq_d₃₂_comp_inv, QuadraticModuleCat.toIsometry_comp, Rep.coe_res_obj_ρ, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, monoidalClosed_uncurry, Rep.diagonalHomEquiv_symm_apply, groupCohomology.H0IsoOfIsTrivial_hom, CondensedMod.isDiscrete_tfae, CoalgCat.MonoidalCategoryAux.associator_hom_toLinearMap, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, groupHomology.mem_cycles₂_iff, Iso.homCongr_eq_arrowCongr, CoextendScalars.smul_apply', groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, groupHomology.cyclesMap_comp_isoCycles₂_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, groupCohomology.d₁₂_hom_apply, instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, groupHomology.comp_d₂₁_eq, PresheafOfModules.pushforward_map_app_apply, groupCohomology.coboundariesToCocycles₁_apply, groupHomology.mapCycles₁_comp_assoc, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₂_isModule, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, PresheafOfModules.sections_property, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, PresheafOfModules.toSheafify_app_apply', PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, Rep.coinvariantsAdjunction_counit_app, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, QuadraticModuleCat.forget₂_map_associator_inv, LinearMap.comp_id_fgModuleCat, RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, groupCohomology.comp_d₁₂_eq, groupCohomology.mem_cocycles₁_of_addMonoidHom, groupCohomology.cocycles₂.d₂₃_apply, groupCohomology.d₀₁_hom_apply, Rep.linearization_single, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, hom_surjective, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CoalgCat.tensorObj_isAddCommGroup, forget₂_addCommGrp_essSurj, groupCohomology.dArrowIso₀₁_inv_right, groupCohomology.map_H0Iso_hom_f_apply, groupCohomology.d₁₂_comp_d₂₃_apply, groupCohomology.H0IsoOfIsTrivial_inv_apply, groupCohomology.eq_d₂₃_comp_inv_assoc, PresheafOfModules.congr_map_apply, PresheafOfModules.freeYonedaEquiv_symm_app, Rep.finsuppToCoinvariantsTensorFree_single, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, PresheafOfModules.restrictScalarsObj_map, groupHomology.chains₁ToCoinvariantsKer_surjective, Rep.coinvariantsTensorFreeLEquiv_symm_apply, TopModuleCat.continuousSMul, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, groupHomology.cycles₁_eq_top_of_isTrivial, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Rep.resCoindAdjunction_unit_app_hom_hom, groupHomology.d₃₂_comp_d₂₁_assoc, groupCohomology.mem_cocycles₁_def, endRingEquiv_symm_apply_hom, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, Rep.homEquiv_apply_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, MonoidalCategory.associator_hom_apply, groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂, CategoryTheory.Iso.toCoalgEquiv_toCoalgHom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, Rep.norm_comm_apply, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasLimit.productLimitCone_cone_π, HasColimit.colimitCocone_ι_app, CoalgCat.moduleCat_of_toModuleCat, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, groupCohomology.coboundaries₁_eq_bot_of_isTrivial, MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, PresheafOfModules.Derivation.postcomp_d_apply, smulShortComplex_X₃_isAddCommGroup, forget₂_addCommGroup_full, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, groupCohomology.cocycles₂_map_one_fst, PresheafOfModules.sectionsMap_coe, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.ρ_hom, Rep.diagonalSuccIsoFree_inv_hom_single_single, groupCohomology.H1IsoOfIsTrivial_inv_apply, PresheafOfModules.Sheafify.map_smul_eq, PresheafOfModules.map_comp_apply, biprodIsoProd_inv_comp_snd_apply, RestrictionCoextensionAdj.counit'_app, groupHomology.chainsMap_f_3_comp_chainsIso₃, PresheafOfModules.pushforward_map_app_apply', groupHomology.mapCycles₁_id_comp_assoc, groupHomology.eq_d₂₁_comp_inv, PresheafOfModules.Derivation.d_mul, isFG_iff, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, groupHomology.mapCycles₁_comp, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Rep.ihom_ev_app_hom, homLinearEquiv_symm_apply, hom_smul, groupCohomology.dArrowIso₀₁_hom_right, uliftFunctorForgetIso_hom_app, Rep.MonoidalClosed.linearHomEquivComm_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom, FGModuleCat.hom_comp, ContinuousCohomology.I_obj_ρ_apply, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, imageIsoRange_hom_subtype, GradedObject.finrankSupport_subset_iff, CategoryTheory.Iso.toIsometryEquiv_toFun, groupHomology.mapCycles₁_comp_i, CoextendScalars.smul_apply, groupCohomology.shortComplexH0_f, binaryProductLimitCone_cone_π_app_right, groupCohomology.cocyclesOfIsCocycle₁_coe, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, HasColimit.colimitCocone_pt_isModule, groupCohomology.coboundaries₂_le_cocycles₂, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, Rep.coindVEquiv_symm_apply_coe, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, imageIsoRange_inv_image_ι_apply, groupCohomology.comp_d₂₃_eq, CondensedMod.isDiscrete_iff_isDiscrete_forget, PresheafOfModules.map_smul, FGModuleCat.FGModuleCatEvaluation_apply, epi_iff_surjective, groupCohomology.coboundaries₂.val_eq_coe, PresheafOfModules.Monoidal.tensorObj_map_tmul, exteriorPower.map_mk, TopModuleCat.ofHom_hom, cokernel_π_cokernelIsoRangeQuotient_hom, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupCohomology.infNatTrans_app, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, hom_inv_apply, groupHomology.mapCycles₂_id_comp, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, monoidalClosed_curry, groupCohomology.d₀₁_apply_mem_cocycles₁, QuadraticModuleCat.instMonoidalCategory.tensorObj_form, CoalgCat.tensorHom_def, Module.Flat.iff_rTensor_preserves_shortComplex_exact, MonoidalCategory.leftUnitor_hom_apply, Rep.indToCoindAux_fst_mul_inv, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.coinvariantsFunctor_obj_carrier, Rep.applyAsHom_comm_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, restrictScalarsId'App_hom_apply, groupCohomology.subtype_comp_d₀₁_apply, ContinuousCohomology.Iobj_ρ_apply, SheafOfModules.pushforwardComp_inv_app_val_app, FilteredColimits.forget_preservesFilteredColimits, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.comp_d₀₁_eq, groupCohomology.cocycles₂_map_one_snd, homAddEquiv_symm_apply_hom, Rep.coinvariantsTensorFreeLEquiv_apply, groupHomology.toCycles_comp_isoCycles₁_hom_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, groupHomology.mapCycles₂_comp_i, localizedModule_isLocalizedModule, range_eq_top_of_epi, groupCohomology.map_H0Iso_hom_f, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, groupHomology.boundariesOfIsBoundary₁_coe, Derivation.d_mul, Rep.indToCoindAux_comm, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, ContinuousCohomology.I_obj_V_isModule, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_left, groupHomology.cyclesIso₀_comp_H0π_apply, CoalgCat.associator_def, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, CondensedMod.epi_iff_surjective_on_stonean, hom_whiskerRight, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, hom_inv_associator, FGModuleCat.hom_id, lof_coprodIsoDirectSum_inv, groupHomology.single_one_fst_sub_single_one_fst_mem_boundaries₂, TopModuleCat.hom_add, BialgCat.forget₂_coalgebra_obj, CoalgCat.MonoidalCategoryAux.tensorObj_comul, CoalgCat.comul_def, inv_hom_apply, forget₂AddCommGroup_preservesLimits, directLimitIsColimit_desc, CategoryTheory.preadditiveYonedaObj_obj_isModule, groupHomology.mapCycles₁_id_comp_apply, MonoidalCategory.rightUnitor_def, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, CategoryTheory.Iso.toLinearEquiv_symm, PresheafOfModules.presheaf_map_apply_coe, smulShortComplex_g, Rep.ofMulDistribMulAction_ρ_apply_apply, Rep.instIsTrivialCarrierVModuleCatOfCompLinearMapIdρ, groupCohomology.instEpiModuleCatH1π, MonoidalCategory.associator_def, groupCohomology.H2π_comp_map, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, groupHomology.π_comp_H2Iso_hom, forget₂_obj, Rep.indResAdjunction_counit_app_hom_hom, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Rep.coindToInd_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, SheafOfModules.pushforwardCongr_hom_app_val_app, hom_whiskerLeft, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, groupHomology.mapCycles₂_comp, comp_apply, restrictScalarsCongr_hom_app, kernelIsoKer_inv_kernel_ι_apply, ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.whiskering_linearYoneda, MonoidalCategory.rightUnitor_hom_apply, groupCohomology.isoCocycles₂_hom_comp_i, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CoalgCat.whiskerRight_def, TopModuleCat.hom_zsmul, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, FilteredColimits.M.mk_map, groupCohomology.π_comp_H0Iso_hom_apply, groupHomology.coe_mapCycles₂, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, CategoryTheory.whiskering_linearCoyoneda₂, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, groupHomology.H1π_comp_map_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, groupCohomology.dArrowIso₀₁_hom_left, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MatrixModCat.toModuleCat_obj_carrier, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, groupCohomology.cocycles₁_map_inv, Rep.freeLiftLEquiv_apply, hom_hom_leftUnitor, groupCohomology.mapCocycles₁_one, PresheafOfModules.surjective_of_epi, adj_homEquiv, instIsScalarTowerLocalizationCarrierLocalizedModule, groupHomology.H2π_comp_map_assoc, Rep.indToCoindAux_mul_fst, hom_hom_rightUnitor, LightCondensed.forget_map_val_app, biprodIsoProd_inv_comp_snd, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, CategoryTheory.Iso.toCoalgEquiv_refl, piIsoPi_inv_kernel_ι_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, Rep.ihom_obj_ρ_apply, ker_eq_bot_of_mono, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, groupHomology.d₁₀ArrowIso_inv_right, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, Rep.finsuppTensorRight_hom_hom, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, groupCohomology.norm_ofAlgebraAutOnUnits_eq, groupCohomology.π_comp_H0Iso_hom_assoc, imageIsoRange_hom_subtype_assoc, groupCohomology.mem_cocycles₂_iff, Rep.tensor_ρ, QuadraticModuleCat.toIsometry_whiskerRight, PresheafOfModules.pushforward_obj_map_apply, groupCohomology.H2π_comp_map_assoc, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, CoalgCat.forget_reflects_isos, Rep.ofDistribMulAction_ρ_apply_apply, groupCohomology.d₀₁_ker_eq_invariants, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, Rep.linearization_η_hom_apply, smulNatTrans_apply_app, FGModuleCat.ihom_obj, TopModuleCat.hom_id, forget_reflectsLimits, Rep.leftRegularHomEquiv_symm_apply, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, groupHomology.H1AddEquivOfIsTrivial_single, groupCohomology.mem_cocycles₁_iff, CoalgCat.ofComonObjCoalgebraStruct_comul, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, groupHomology.range_d₁₀_eq_coinvariantsKer, QuadraticModuleCat.toIsometry_tensorHom, PresheafOfModules.unitHomEquiv_apply_coe, groupCohomology.inhomogeneousCochains.d_comp_d, FreeMonoidal.εIso_inv_freeMk, groupHomology.isoCycles₂_hom_comp_i_apply, Rep.ofModuleMonoidAlgebra_obj_ρ, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, QuadraticModuleCat.toIsometry_hom_leftUnitor, Rep.coinvariantsShortComplex_f, SheafOfModules.pushforwardCongr_inv_app_val_app, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, QuadraticModuleCat.toIsometry_hom_rightUnitor, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles, RestrictionCoextensionAdj.unit'_app, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierOfCarrierStalkAbPresheafPrimeComplAsIdealHomToStalk, groupHomology.eq_d₂₁_comp_inv_assoc, imageIsoRange_inv_image_ι, smulShortComplex_X₃_carrier, free_η_freeMk, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, ContinuousCohomology.I_map_hom, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, groupHomology.inhomogeneousChains.d_single, groupCohomology.coboundariesOfIsCoboundary₁_coe, exteriorPower.iso₁_hom_apply, TopModuleCat.freeMap_map, Representation.coind'_apply_apply, groupCohomology.d₁₂_comp_d₂₃_assoc, QuadraticModuleCat.Hom.toIsometry_injective, CoalgCat.Hom.toCoalgHom_injective, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, hom_inv_rightUnitor, ExtendScalars.smul_tmul, hom_sum, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, CategoryTheory.Iso.toCoalgEquiv_trans, groupHomology.mapCycles₂_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, Rep.coindIso_inv_hom_hom, hom_nsmul, groupCohomology.map_id_comp_H0Iso_hom_apply, groupCohomology.cocycles₁_map_mul_of_isTrivial, forget_obj, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.chainsMap_id_f_hom_eq_mapRange, PresheafOfModules.toPresheaf_map_app_apply, groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupCohomology.map_id_comp_H0Iso_hom, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mapCycles₁_id_comp, Rep.indToCoindAux_mul_snd, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, CategoryTheory.Iso.toIsometryEquiv_refl, QuadraticModuleCat.toIsometry_inv_rightUnitor, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, ExtendScalars.map_tmul, QuadraticModuleCat.cliffordAlgebra_map, FilteredColimits.forget_reflectsFilteredColimits, groupCohomology.cocyclesOfIsMulCocycle₂_coe, LinearMap.id_moduleCat_comp, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, QuadraticModuleCat.toIsometry_whiskerLeft, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.Iso.toLinearEquiv_apply, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, groupHomology.isoShortComplexH1_inv, groupCohomology.coboundariesOfIsMulCoboundary₁_coe, SheafOfModules.pushforwardComp_hom_app_val_app, groupHomology.eq_d₁₀_comp_inv_assoc, groupCohomology.d₁₂_comp_d₂₃, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, Rep.linearization_obj_ρ, Rep.toCoinvariantsMkQ_hom, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, MonoidalCategory.tensorObj, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, imageIsoRange_inv_image_ι_assoc, MonoidalCategory.rightUnitor_inv_apply, groupCohomology.H1π_eq_zero_iff, Rep.invariantsAdjunction_counit_app_hom, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, groupCohomology.coboundaries₁.val_eq_coe, groupHomology.d₃₂_single_one_fst, inhomogeneousCochains.d_hom_apply, CoalgCat.MonoidalCategoryAux.counit_tensorObj, Rep.coind'_ext_iff, CoalgCat.counit_def, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, TopModuleCat.instPreservesLimitsOfShapeTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitsOfShapeOfModuleCatForgetLinearMap, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, groupHomology.d₂₁_comp_d₁₀, PresheafOfModules.Elements.fromFreeYoneda_app_apply, binaryProductLimitCone_cone_π_app_left, HasColimit.coconePointSMul_apply, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, kernelIsoKer_hom_ker_subtype, smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, hom_add, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, groupCohomology.cocyclesMk₁_eq, AlgCat.forget₂_module_obj, MonoidalCategory.leftUnitor_inv_apply, ι_coprodIsoDirectSum_hom, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, SheafOfModules.relationsOfIsCokernelFree_I, MonModuleEquivalenceAlgebra.algebraMap, MonoidalCategory.tensorμ_apply, groupHomology.cyclesOfIsCycle₁_coe, Rep.quotientToInvariantsFunctor_obj_V, MonoidalCategory.tensorObj_isModule, groupHomology.inhomogeneousChains.ext_iff, MonoidalCategory.tensorObj_isAddCommGroup, groupHomology.d₂₁_apply_mem_cycles₁, groupCohomology.coboundariesToCocycles₂_apply, ihom_map_apply, MonModuleEquivalenceAlgebra.inverseObj_mul, ihom_coev_app, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.cocyclesOfIsMulCocycle₁_coe, groupCohomology.H2π_eq_zero_iff, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_left, groupCohomology.mapCocycles₁_comp_i_assoc, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, groupCohomology.cocycles₁.val_eq_coe, groupCohomology.H1π_comp_map_apply, free_shortExact, Rep.leftRegularHom_hom_single, groupCohomology.cocycles₁_map_one, groupHomology.eq_d₃₂_comp_inv_assoc, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, hom_hom_associator, CoalgCat.forget₂_obj, groupCohomology.π_comp_H2Iso_hom_assoc, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, Rep.finsuppTensorRight_inv_hom, Rep.coinvariantsMk_app_hom, Rep.ihom_obj_V_isAddCommGroup, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, CategoryTheory.ShortComplex.moduleCat_exact_iff, groupHomology.mapCycles₂_hom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, mkOfSMul_smul, MatrixModCat.isScalarTower_toModuleCat, restrictScalars.smul_def, CoalgCat.whiskerLeft_def, TopModuleCat.hom_sub, kernelIsoKer_hom_ker_subtype_apply, QuadraticModuleCat.toIsometry_id, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, Rep.coindVEquiv_apply_hom, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, groupHomology.H1π_eq_zero_iff, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, groupHomology.π_comp_H1Iso_hom_assoc, LightCondMod.hom_naturality_apply, TopModuleCat.forget₂_TopCat_obj, groupHomology.chainsMap_f_2_comp_chainsIso₂, groupHomology.d₂₁_single_one_fst, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, HasLimit.productLimitCone_cone_pt_isModule, groupHomology.H2π_comp_map, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, TopModuleCat.hom_nsmul, groupCohomology.cocycles₂.val_eq_coe, groupCohomology.eq_d₂₃_comp_inv, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupHomology.H1π_comp_map_assoc, Rep.ihom_map_hom, groupHomology.instEpiModuleCatH1π, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, MonoidalCategory.whiskerRight_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, Rep.finsuppTensorLeft_inv_hom, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, CoalgCat.forget₂_map, groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂, Rep.unit_iso_comm, Rep.leftRegularHomEquiv_symm_single, inhomogeneousCochains.d_eq, groupHomology.instEpiModuleCatH2π, piIsoPi_hom_ker_subtype, hom_id, groupCohomology.cocyclesMk₂_eq, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.H1π_comp_map, groupHomology.chainsMap_f_hom, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, MonoidalCategory.tensorUnit_isModule, piIsoPi_inv_kernel_ι, Rep.norm_hom, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.indResAdjunction_unit_app_hom_hom, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, groupHomology.boundariesOfIsBoundary₂_coe, groupHomology.cyclesMk₁_eq, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, LightCondensed.ihom_map_val_app, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, TopModuleCat.cokerπ_surjective, FreeMonoidal.μIso_inv_freeMk, uliftFunctor_map, Rep.Action_ρ_eq_ρ, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, ofHom_hom, Rep.coindMap_hom, groupHomology.mapCycles₂_id_comp_apply, Rep.trivial_def, groupCohomology.cocycles₂_ext_iff, CategoryTheory.ShortComplex.moduleCatMk_X₁_isModule, instFiniteCarrierObjModuleCatIsFG, Rep.MonoidalClosed.linearHomEquiv_hom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, Rep.invariantsAdjunction_homEquiv_apply_hom, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, localizedModuleMap_hom_apply, Rep.hom_comm_apply, SheafOfModules.pushforwardNatTrans_app_val_app, groupHomology.H2π_comp_map_apply, Hom.hom₂_apply, CategoryTheory.Iso.toIsometryEquiv_invFun, TopModuleCat.hom_smul, HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, uliftFunctor_obj, forget₂_addCommGrp_additive, Module.Flat.iff_preservesFiniteLimits_tensorLeft, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, CoalgCat.MonoidalCategoryAux.comul_tensorObj, groupCohomology.coboundaries₁_ext_iff, Rep.finsuppTensorLeft_hom_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, projective_of_module_projective, MatrixModCat.toModuleCat_map, MonoidalCategory.leftUnitor_def, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, binaryProductLimitCone_isLimit_lift, TopModuleCat.instPreservesLimitsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, homLinearEquiv_apply, Rep.coinvariantsTensorMk_apply, TopModuleCat.kerι_apply, Rep.indMap_hom, groupHomology.isoCycles₁_hom_comp_i_assoc, Rep.homEquiv_symm_apply_hom, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, CategoryTheory.linearYoneda_obj_obj_isModule, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Rep.invariantsFunctor_map_hom, Iso.conj_eq_conj, groupHomology.d₁₀_eq_zero_of_isTrivial, CoalgCat.toComon_map_hom, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, groupCohomology.d₀₁_comp_d₁₂_assoc, MonoidalCategory.tensorObj_def, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, groupHomology.d₂₁_single_one_snd, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, CategoryTheory.ShortComplex.moduleCatMk_X₃_isModule, biprodIsoProd_inv_comp_fst, groupHomology.π_map_apply, CoalgCat.rightUnitor_def, BialgCat.forget₂_coalgebra_map, groupHomology.d₃₂_comp_d₂₁, groupHomology.d₃₂_single_one_snd, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, QuadraticModuleCat.cliffordAlgebra_obj_carrier, groupHomology.π_comp_H2Iso_hom_apply, CoalgCat.tensorObj_carrier, SheafOfModules.relationsOfIsCokernelFree_s, forget₂_reflectsLimits, FDRep.of_ρ, forget₂PreservesColimitsOfShape, MatrixModCat.toModuleCat_obj_isAddCommGroup, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, Rep.ihom_coev_app_hom, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, Rep.leftRegularHomEquiv_apply, restrictScalars.smul_def', PresheafOfModules.pushforward_obj_map_apply', groupHomology.isoCycles₁_inv_comp_iCycles, free_shortExact_rank_add, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, FGModuleCat.FGModuleCatEvaluation_apply', forget₂AddCommGroup_reflectsLimit, groupHomology.isoShortComplexH2_inv, groupHomology.coe_mapCycles₁, groupHomology.toCycles_comp_isoCycles₁_hom, hom_inv_leftUnitor, TopModuleCat.instReflectsIsomorphismsTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier, groupCohomology.d₀₁_comp_d₁₂_apply, free_map_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, Representation.linHom.mem_invariants_iff_comm, groupHomology.mapCycles₂_comp_i_apply, binaryProductLimitCone_cone_pt, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ofHom₂_hom_apply_hom, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, groupHomology.boundariesToCycles₂_apply, groupCohomology.subtype_comp_d₀₁, groupHomology.cyclesOfIsCycle₂_coe, Rep.freeLift_hom, groupHomology.isoCycles₂_hom_comp_i, CoalgCat.tensorObj_instCoalgebra, groupHomology.π_comp_H1Iso_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.π_map_apply, Rep.indToCoindAux_snd_mul_inv, hom_sub, CoalgCat.ofComonObjCoalgebraStruct_counit, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, Rep.res_obj_ρ, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, ofHom₂_compr₂, Algebra.instSMulCommClassCarrier, PresheafOfModules.freeYonedaEquiv_comp, forget₂AddCommGroup_preservesLimit, groupCohomology.coboundaries₁_le_cocycles₁, Rep.ihom_obj_V_isModule, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, CoalgCat.tensorObj_isModule, FreeMonoidal.εIso_hom_one, groupHomology.d₁₀ArrowIso_hom_right, QuadraticModuleCat.toIsometry_inv_leftUnitor, Rep.freeLift_hom_single_single, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, groupHomology.single_one_mem_boundaries₁, mono_iff_ker_eq_bot, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, groupHomology.π_comp_H1Iso_inv_apply, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.isoCocycles₂_hom_comp_i_apply, extendRestrictScalarsAdj_unit_app_apply, hom_bijective, Rep.diagonalHomEquiv_apply, groupHomology.d₂₁_single, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, SheafOfModules.Presentation.IsFinite.finite_relations, Rep.freeLiftLEquiv_symm_apply, groupHomology.inhomogeneousChains.d_eq, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, groupCohomology.coboundaries₂_ext_iff, groupHomology.d₁₀_comp_coinvariantsMk_assoc, MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, Rep.indToCoindAux_of_not_rel, groupCohomology.cocyclesOfIsCocycle₂_coe, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Rep.applyAsHom_hom, CoalgCat.toCoalgHom_id, CoalgCat.tensorUnit_isModule, forget_map, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupCohomology.H1π_comp_map, TopModuleCat.hom_comp, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, smulShortComplex_X₃_isModule, Rep.indResHomEquiv_apply_hom, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, directLimitCocone_pt_isModule, CommRingCat.KaehlerDifferential.ext_iff, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, PresheafOfModules.germ_ringCat_smul, groupCohomology.cocyclesMk₀_eq, endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, groupHomology.single_mem_cycles₂_iff, groupCohomology.isoShortComplexH1_inv, groupHomology.boundaries₁_le_cycles₁, CoalgCat.toCoalgHom_comp, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, Rep.diagonalSuccIsoFree_hom_hom_single, CoalgCat.MonoidalCategoryAux.rightUnitor_hom_toLinearMap, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, sMulCommClass_mk, QuadraticModuleCat.moduleCat_of_toModuleCat, PresheafOfModules.germ_smul, CoalgCat.leftUnitor_def, hom_neg, Rep.ihom_obj_ρ, instInvertibleCarrierOutModuleCatValSkeleton, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, Rep.free_ext_iff, PresheafOfModules.toSheafify_app_apply, MonoidalCategory.whiskerRight_def, isScalarTower_of_algebra_moduleCat, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, groupCohomology.cocycles₁_ext_iff, Algebra.instIsScalarTowerCarrier, groupCohomology.map_H0Iso_hom_f_assoc, ofHom_apply, TannakaDuality.FiniteGroup.ofRightFDRep_hom, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, PresheafOfModules.pushforward₀_obj_obj_isModule, simple_iff_isSimpleModule', restrictScalarsCongr_inv_app, groupCohomology.eq_d₁₂_comp_inv_assoc, Representation.linHom.invariantsEquivRepHom_apply_hom, groupCohomology.H1InfRes_f, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, TopModuleCat.hom_neg, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, forget₂AddCommGroupIsEquivalence, groupHomology.d₁₀ArrowIso_inv_left, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.single_mem_cycles₁_iff, Rep.coinvariantsFunctor_map_hom, groupHomology.d₂₁_single_ρ_add_single_inv_mul, HasLimit.productLimitCone_isLimit_lift, hom_injective, MonoidalCategory.tensorObj_carrier, Rep.linearization_map_hom_single, groupCohomology.isoShortComplexH2_inv, CategoryTheory.preadditiveCoyoneda_obj, groupCohomology.map_id_comp_H0Iso_hom_assoc, groupCohomology.isoCocycles₂_hom_comp_i_assoc, groupHomology.eq_d₁₀_comp_inv_apply, Rep.ihom_obj_V_carrier, LinearEquiv.toFGModuleCatIso_inv, ContinuousCohomology.const_app_hom, semilinearMapAddEquiv_apply, CoextendScalars.map'_hom_apply_apply, Rep.coindIso_hom_hom_hom, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, groupHomology.H0π_comp_H0Iso_hom_apply, Rep.barComplex.d_single, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, Rep.mono_iff_injective, CategoryTheory.linearCoyoneda_obj_obj_isModule, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupHomology.d₂₁_comp_d₁₀_assoc, groupCohomology.coe_mapCocycles₂, groupCohomology.eq_d₀₁_comp_inv_assoc, isSimpleModule_of_simple, toKernelSubobject_arrow, CategoryTheory.Iso.toLinearMap_toLinearEquiv, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, groupCohomology.isoCocycles₁_hom_comp_i_assoc, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, groupHomology.mapCycles₁_quotientGroupMk'_epi, groupHomology.mapCycles₁_comp_i_assoc, groupHomology.H0π_comp_map_apply, restrictScalarsId'App_inv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, PresheafOfModules.Sheafify.SMulCandidate.h, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, groupHomology.π_comp_H2Iso_inv_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, groupCohomology.coboundariesOfIsCoboundary₂_coe, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, restrictScalarsComp'App_inv_apply, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mem_cycles₁_iff, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i, groupHomology.boundariesToCycles₁_apply, groupHomology.single_mem_cycles₂_iff_inv, groupHomology.d₁₀_single, TopModuleCat.hom_forget₂_TopCat_map, ihom_ev_app, groupCohomology.cocycles₁.d₁₂_apply, Rep.indResHomEquiv_symm_apply_hom, groupHomology.isoCycles₂_hom_comp_i_assoc, FilteredColimits.colimit_add_mk_eq, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, free_hom_ext_iff, CategoryTheory.Iso.toIsometryEquiv_symm, groupHomology.H2π_eq_zero_iff, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.Iso.toIsometryEquiv_trans, MonoidalCategory.associator_inv_apply, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, QuadraticModuleCat.hom_hom_associator, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.H1π_eq_iff, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, CoextendScalars.map_apply, groupHomology.chainsMap_f, Rep.quotientToCoinvariantsFunctor_obj_V, SheafOfModules.unitHomEquiv_apply_coe, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom, QuadraticModuleCat.hom_inv_associator, forget₂_map, groupCohomology.d₀₁_eq_zero, toMatrixModCat_obj_isModule
mkOfSMul 📖	CompOp	2 math math: HasColimit.colimitCocone_ι_app, mkOfSMul_smul
mkOfSMul' 📖	CompOp	2 math math: mkOfSMul'_smul, HasColimit.colimitCocone_pt_carrier
moduleCategory 📖	CompOp	1589 math math: HasColimit.colimitCocone_pt_isAddCommGroup, instIsRightAdjointCoextendScalars, instPreservesMonomorphismsRestrictScalars, PresheafOfModules.Monoidal.tensorObj_obj, groupHomology.mapShortComplexH2_τ₁, Rep.resCoindHomEquiv_symm_apply_hom, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Representation.repOfTprodIso_inv_apply, Rep.resCoindHomEquiv_apply_hom, groupCohomology.instEpiModuleCatH2π, groupCohomology.mapShortComplexH1_τ₂, hom_zero, groupHomology.π_comp_H2Iso_hom_assoc, instReflectsIsomorphismsForgetLinearMapIdCarrier, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.linearCoyoneda_obj_additive, instFullUliftFunctor, forget_preservesLimits, directLimitDiagram_obj_isModule, CommRingCat.KaehlerDifferential.map_d, CategoryTheory.preadditiveCoyonedaObj_map, MonoidalCategory.braiding_hom_apply, Rep.coe_linearization_obj_ρ, biproductIsoPi_inv_comp_π, simple_of_finrank_eq_one, FilteredColimits.colimit_smul_mk_eq, groupHomology.mapCycles₂_comp_assoc, restrictScalars.map_apply, Condensed.instAB4StarCondensedMod, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom, forget₂_reflectsLimitsOfSize, CategoryTheory.additive_yonedaObj, groupCohomology.toCocycles_comp_isoCocycles₁_hom, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.linearCoyoneda_obj_obj_carrier, Rep.MonoidalClosed.linearHomEquiv_symm_hom, projective_of_free, groupCohomology.isoCocycles₁_hom_comp_i_apply, instEssentiallySmallFGModuleCat, groupHomology.map₁_quotientGroupMk'_epi, groupCohomology.mem_cocycles₂_def, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, MoritaEquivalence.linear, groupHomology.coinfNatTrans_app, groupHomology.mapShortComplexH2_id, forget_preservesLimitsOfSize, groupCohomology.d₂₃_hom_apply, restrictScalarsCongr_symm, LightCondensed.ihomPoints_apply, LinearMap.id_fgModuleCat_comp, restrictScalarsId'App_inv_naturality_assoc, groupHomology.d₁₀_single_one, groupHomology.shortComplexH1_f, FDRep.char_tensor, groupHomology.boundaries₂_le_cycles₂, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, groupCohomology.inhomogeneousCochains.d_def, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, PresheafOfModules.add_app, FGModuleCat.hom_hom_id, Rep.diagonalSuccIsoFree_inv_hom_single, CondensedMod.IsSolid.isIso_solidification_map, groupCohomology.cocyclesMap_id_comp_assoc, groupHomology.map₁_one, groupCohomology.d₀₁_comp_d₁₂, Representation.repOfTprodIso_apply, freeHomEquiv_apply, epi_as_hom''_mkQ, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, Rep.coindResAdjunction_counit_app, forget₂AddCommGroup_preservesLimitsOfSize, toMatrixModCat_map, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, LightCondensed.forget_obj_val_map, groupCohomology.cocyclesIso₀_hom_comp_f, Rep.resCoindAdjunction_counit_app_hom_hom, groupHomology.d₃₂_single, CategoryTheory.Abelian.FreydMitchell.instFaithfulModuleCatEmbeddingRingFunctor, groupCohomology.eq_d₀₁_comp_inv, extendScalarsId_hom_app_one_tmul, groupCohomology.H1π_comp_map_assoc, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, Rep.leftRegularHom_hom, PresheafOfModules.restrictScalars_map_app, groupHomology.mapShortComplexH1_zero, groupCohomology.π_comp_H0Iso_hom, FDRep.endRingEquiv_symm_comp_ρ, ofHom_comp, groupHomology.H0IsoOfIsTrivial_inv_eq_π, groupCohomology.π_comp_H1Iso_hom_assoc, ι_coprodIsoDirectSum_hom_apply, restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, groupHomology.cyclesMap_id_comp, LightCondensed.ihomPoints_symm_comp, Rep.indFunctor_obj, isZero_iff_subsingleton, groupHomology.mapShortComplexH2_zero, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_carrier, Rep.indToCoindAux_self, Condensed.instAB5CondensedMod, groupCohomology.instPreservesZeroMorphismsRepCochainComplexModuleCatNatCochainsFunctor, groupCohomology.mapCocycles₂_comp_i, PresheafOfModules.evaluation_preservesColimitsOfShape, AlternatingMap.postcomp_apply, groupHomology.H1CoresCoinf_exact, groupHomology.eq_d₃₂_comp_inv, FGModuleCat.instHasColimitsOfShapeOfFinCategory, PresheafOfModules.comp_app, CategoryTheory.ShortComplex.moduleCatMk_X₁_isAddCommGroup, Rep.indCoindNatIso_hom_app, groupHomology.chainsMap_id, instSmallUnitsSkeletonModuleCat, Rep.coe_res_obj_ρ, Rep.invariantsFunctor_obj_carrier, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, Rep.barComplex.d_def, monoidalClosed_uncurry, Rep.diagonalHomEquiv_symm_apply, groupCohomology.H0IsoOfIsTrivial_hom, matrixEquivalence_inverse, TannakaDuality.FiniteGroup.forget_obj, CondensedMod.isDiscrete_tfae, CategoryTheory.linearYoneda_obj_map, Rep.coindFunctor_map, hasLimits', CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, groupHomology.mem_cycles₂_iff, Iso.homCongr_eq_arrowCongr, CoextendScalars.smul_apply', groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_g, groupHomology.cyclesMap_comp_isoCycles₂_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isModule, directLimitCocone_pt_carrier, toMatrixModCat_obj_carrier, groupCohomology.d₁₂_hom_apply, preservesFiniteLimits_extendScalars_of_flat, instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, instAB4StarModuleCat, groupHomology.comp_d₂₁_eq, PresheafOfModules.pushforward_map_app_apply, Rep.instIsLeftAdjointSubtypeMemSubgroupCoindFunctorSubtype, CategoryTheory.preadditiveYonedaObj_obj_carrier, groupCohomology.coboundariesToCocycles₁_apply, Rep.instIsRightAdjointCoindFunctor, groupHomology.mapCycles₁_comp_assoc, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₂_isModule, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, CondensedMod.LocallyConstant.instFullModuleCatFunctor, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, Rep.instIsTrivialObjModuleCatTrivialFunctor, PresheafOfModules.sections_property, groupHomology.H0π_comp_map, linearEquivIsoModuleIso_hom, groupHomology.H1CoresCoinf_X₃, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, groupCohomology.mapShortComplexH1_τ₃, AlgebraicGeometry.instIsLeftAdjointModuleCatCarrierModulesSpecOfFunctor, PresheafOfModules.toSheafify_app_apply', AlgebraicGeometry.tilde.map_id, PresheafOfModules.instPreservesLimitsOfShapeModuleCatCarrierObjOppositeRingCatEvaluation, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, Rep.coinvariantsAdjunction_counit_app, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, LightCondMod.instPreservesEpimorphismsLightCondSetForget, forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, groupHomology.map_id, QuadraticModuleCat.forget₂_map_associator_inv, LinearMap.comp_id_fgModuleCat, HasColimit.instHasColimit, RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, groupCohomology.cochainsMap_comp, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, AlgebraicGeometry.tilde.map_sub, groupCohomology.comp_d₁₂_eq, toMatrixModCat_obj_isAddCommGroup, groupCohomology.mem_cocycles₁_of_addMonoidHom, groupCohomology.cocycles₂.d₂₃_apply, groupCohomology.d₀₁_hom_apply, Rep.linearization_single, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.π_comp_H1Iso_inv, groupHomology.d₃₂_single_one_thd, CategoryTheory.ShortComplex.moduleCatMk_g, LightCondMod.isDiscrete_tfae, restrictScalarsComp'_inv_app, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, groupHomology.coresNatTrans_app, PresheafOfModules.free_map_app, groupHomology.instPreservesZeroMorphismsRepModuleCatFunctor, forget₂_addCommGrp_essSurj, groupCohomology.dArrowIso₀₁_inv_right, groupCohomology.map_H0Iso_hom_f_apply, shortExact_projectiveShortComplex, groupCohomology.d₁₂_comp_d₂₃_apply, groupCohomology.H0IsoOfIsTrivial_inv_apply, groupCohomology.eq_d₂₃_comp_inv_assoc, PresheafOfModules.congr_map_apply, groupCohomology.congr, CategoryTheory.Abelian.freyd_mitchell, PresheafOfModules.freeYonedaEquiv_symm_app, Rep.finsuppToCoinvariantsTensorFree_single, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatCondensedDiscrete, groupHomology.mapShortComplexH1_τ₂, PresheafOfModules.restrictScalarsObj_map, PresheafOfModules.forgetToPresheafModuleCatObj_map, groupHomology.chains₁ToCoinvariantsKer_surjective, enoughProjectives, restrictScalarsId'App_hom_naturality, Rep.coinvariantsTensorFreeLEquiv_symm_apply, Rep.standardComplex.d_eq, LinearEquiv.toModuleIso_inv, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, SheafOfModules.evaluationPreservesLimitsOfShape, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, forget₂AddCommGroup_reflectsLimitOfShape, exteriorPower.iso₀_hom_naturality, forget_reflectsLimitsOfSize, groupHomology.cycles₁_eq_top_of_isTrivial, instIsEquivalenceFGModuleCatUlift, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, Rep.resCoindAdjunction_unit_app_hom_hom, restrictScalars_isEquivalence_of_ringEquiv, groupHomology.d₃₂_comp_d₂₁_assoc, groupCohomology.mem_cocycles₁_def, CoalgCat.comonEquivalence_inverse, Rep.trivial_projective_of_subsingleton, endRingEquiv_symm_apply_hom, FGModuleCat.instFiniteHomModuleCatObjIsFG, Rep.instEpiModuleCatHom, restrictScalarsComp'_hom_app, groupHomology.H1CoresCoinfOfTrivial_X₁, Rep.homEquiv_apply_hom, groupHomology.chainsMap_id_f_map_mono, FilteredColimits.colimit_zero_eq, groupCohomology.mapShortComplexH2_comp_assoc, Rep.FiniteCyclicGroup.chainComplexFunctor_obj, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, instHasFiniteColimits, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, PresheafOfModules.id_app, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.full, MonoidalCategory.associator_hom_apply, groupHomology.single_one_snd_sub_single_one_fst_mem_boundaries₂, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, Rep.norm_comm_apply, AlgebraicGeometry.instAdditiveModuleCatCarrierModulesSpecOfFunctor, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasLimit.productLimitCone_cone_π, HasColimit.colimitCocone_ι_app, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, PresheafOfModules.restrictScalarsObj_obj, groupCohomology.coboundaries₁_eq_bot_of_isTrivial, instHasSeparatorModuleCatOfSmall, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, instAdditiveLocalizationLocalizedModule_functor, MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, groupCohomology.instMonoModuleCatFH1InfRes, smulShortComplex_X₃_isAddCommGroup, forget₂_addCommGroup_full, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, hasLimitsOfSize, groupCohomology.cocycles₂_map_one_fst, Rep.indCoindIso_inv_hom_hom, PresheafOfModules.sectionsMap_coe, groupCohomology.mapCocycles₂_comp_i_assoc, Rep.free_projective, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.ρ_hom, Rep.diagonalSuccIsoFree_inv_hom_single_single, groupCohomology.H1IsoOfIsTrivial_inv_apply, Rep.instPreservesProjectiveObjectsActionModuleCatSubtypeMemSubgroupResSubtype, groupHomology.π_comp_H2Iso_inv_assoc, instPreservesFiniteColimitsUliftFunctor, PresheafOfModules.map_comp_apply, biprodIsoProd_inv_comp_snd_apply, RestrictionCoextensionAdj.counit'_app, groupHomology.chainsMap_f_3_comp_chainsIso₃, PresheafOfModules.pushforward_map_app_apply', groupHomology.mapCycles₁_id_comp_assoc, groupHomology.eq_d₂₁_comp_inv, groupHomology.shortComplexH2_f, CoalgCat.comonEquivalence_counitIso, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, CategoryTheory.linearYoneda_obj_obj_carrier, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, groupHomology.mapCycles₁_comp, groupHomology.map_comp, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Rep.ihom_ev_app_hom, homLinearEquiv_symm_apply, Profinite.NobelingProof.succ_exact, hom_smul, groupCohomology.dArrowIso₀₁_hom_right, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, groupCohomology.π_map_assoc, Rep.MonoidalClosed.linearHomEquivComm_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom, CompHausLike.LocallyConstantModule.functor_map_val, Rep.coe_linearization_obj, Rep.instIsRightAdjointModuleCatInvariantsFunctor, groupCohomology.map_comp, FGModuleCat.hom_comp, SheafOfModules.evaluationPreservesLimitsOfSize, groupHomology.map_id_comp, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, CategoryTheory.faithful_linearYoneda, imageIsoRange_hom_subtype, groupHomology.mapCycles₁_comp_i, CoextendScalars.smul_apply, Rep.coinvariantsTensorIndIso_inv, groupCohomology.shortComplexH0_f, binaryProductLimitCone_cone_π_app_right, groupCohomology.shortComplexH0_g, groupCohomology.cocyclesOfIsCocycle₁_coe, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, groupHomology.functor_obj, PresheafOfModules.zsmul_app, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, matrixEquivalence_functor, HasColimit.colimitCocone_pt_isModule, groupCohomology.shortComplexH1_f, hasLimits, groupCohomology.coboundaries₂_le_cocycles₂, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.linearCoyoneda_obj_obj_isAddCommGroup, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, groupHomology.inhomogeneousChains.d_def, PresheafOfModules.isoMk_hom_app, Rep.coindVEquiv_symm_apply_coe, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapId, restrictScalarsId'App_inv_naturality, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, imageIsoRange_inv_image_ι_apply, Rep.homEquiv_def, Rep.indCoindIso_hom_hom_hom, CategoryTheory.preadditiveYonedaMap_app, groupCohomology.comp_d₂₃_eq, CondensedMod.isDiscrete_iff_isDiscrete_forget, PresheafOfModules.map_smul, FGModuleCat.FGModuleCatEvaluation_apply, epi_iff_surjective, restrictScalarsId'_inv_app, groupCohomology.coboundaries₂.val_eq_coe, AlgebraicGeometry.instFullModuleCatCarrierModulesSpecOfFunctor, PresheafOfModules.Monoidal.tensorObj_map_tmul, exteriorPower.map_mk, cokernel_π_cokernelIsoRangeQuotient_hom, extendScalars_assoc_assoc, groupHomology.H1CoresCoinf_X₁, Rep.ofModuleMonoidAlgebra_obj_coe, groupHomology.single_one_fst_sub_single_one_snd_mem_boundaries₂, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, groupCohomology.infNatTrans_app, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, hom_inv_apply, groupHomology.mapCycles₂_id_comp, Rep.diagonal_succ_projective, CategoryTheory.ShortComplex.moduleCatMk_X₃_isAddCommGroup, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, monoidalClosed_curry, groupCohomology.d₀₁_apply_mem_cocycles₁, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc, exteriorPower.iso₁_hom_naturality, hasColimitsOfSize, PresheafOfModules.instPreservesLimitsOfSizeModuleCatCarrierObjOppositeRingCatEvaluation, Module.Flat.iff_rTensor_preserves_shortComplex_exact, groupHomology.cyclesMap_comp_assoc, MonoidalCategory.leftUnitor_hom_apply, Rep.indToCoindAux_fst_mul_inv, Rep.instIsLeftAdjointActionModuleCatRes, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.coinvariantsFunctor_obj_carrier, Rep.applyAsHom_comm_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupHomology.chainsMap_f_single, restrictScalarsId'App_hom_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, groupCohomology.subtype_comp_d₀₁_apply, SheafOfModules.pushforwardComp_inv_app_val_app, LightCondensed.internallyProjective_iff_tensor_condition, FilteredColimits.forget_preservesFilteredColimits, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.cochainsMap_f_map_epi, groupCohomology.comp_d₀₁_eq, FGModuleCat.instIsMonoidalClosedModuleCatIsFG, Rep.instProjective, groupCohomology.cocycles₂_map_one_snd, restrictScalarsId'App_hom_naturality_assoc, homAddEquiv_symm_apply_hom, LinearMap.shortExact_shortComplexKer, Rep.coinvariantsTensorFreeLEquiv_apply, groupHomology.coinvariantsMk_comp_H0Iso_inv, image.lift_fac, groupHomology.toCycles_comp_isoCycles₁_hom_apply, TannakaDuality.FiniteGroup.sumSMulInv_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, CategoryTheory.ShortComplex.moduleCatMk_X₃_carrier, groupHomology.mapCycles₂_comp_i, Rep.coinvariantsTensorIndIso_hom, groupCohomology.map_H0Iso_hom_f, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, Rep.barResolution_complex, ExtendScalars.map'_id, groupHomology.boundariesOfIsBoundary₁_coe, PresheafOfModules.freeObj_map, instPreservesFiniteColimitsLocalizationLocalizedModule_functor, FDRep.instFiniteDimensionalCarrierVFGModuleCat, FGModuleCat.instFiniteHom, groupCohomology.cochainsMap_zero, Rep.indToCoindAux_comm, smulShortComplex_X₁, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, groupHomology.map_comp_assoc, Rep.coinvariantsTensorIndNatIso_inv_app, AlgebraicGeometry.tilde.isoTop_hom, Tilde.toOpen_res, groupHomology.cyclesIso₀_comp_H0π_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, CondensedMod.epi_iff_surjective_on_stonean, FDRep.average_char_eq_finrank_invariants, hom_whiskerRight, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv, hom_inv_associator, PresheafOfModules.instEpiModuleCatCarrierObjOppositeRingCatApp, FGModuleCat.hom_id, Rep.toAdditive_symm_apply, groupCohomology.H1InfRes_X₂, lof_coprodIsoDirectSum_inv, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, groupCohomology.map₁_one, Rep.coindResAdjunction_unit_app, groupHomology.single_one_fst_sub_single_one_fst_mem_boundaries₂, CategoryTheory.linearYoneda_map_app, instAB4ModuleCat, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, CoalgCat.comul_def, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i, inv_hom_apply, forget₂AddCommGroup_preservesLimits, CategoryTheory.Abelian.full_comp_preadditiveCoyonedaObj, directLimitIsColimit_desc, CategoryTheory.preadditiveYonedaObj_obj_isModule, groupHomology.mapCycles₁_id_comp_apply, MonoidalCategory.rightUnitor_def, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, groupHomology.H1CoresCoinf_g, CategoryTheory.Iso.toLinearEquiv_symm, groupCohomology.cochainsMap_id_comp, PresheafOfModules.presheaf_map_apply_coe, smulShortComplex_g, directLimitCocone_pt_isAddCommGroup, Rep.ofMulDistribMulAction_ρ_apply_apply, groupCohomology.map_id, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.full_embedding, groupCohomology.mapShortComplexH2_comp, ExtendScalars.map'_comp, groupCohomology.shortComplexH2_f, CategoryTheory.linearYoneda_obj_obj_isAddCommGroup, simple_iff_isSimpleModule, restrictScalarsComp'App_hom_naturality_assoc, Rep.instIsTrivialCarrierVModuleCatOfCompLinearMapIdρ, groupCohomology.instEpiModuleCatH1π, MonoidalCategory.associator_def, groupHomology.H1CoresCoinfOfTrivial_X₂, groupHomology.H1CoresCoinf_X₂, IsProjective.iff_projective, groupCohomology.H2π_comp_map, groupCohomology.cochainsMap_comp_assoc, TopModuleCat.instIsRightAdjointModuleCatIndiscrete, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, groupHomology.π_comp_H2Iso_hom, forget₂_obj, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditive_yoneda_obj', TopModuleCat.instIsLeftAdjointModuleCatWithModuleTopology, Rep.indResAdjunction_counit_app_hom_hom, FDRep.hom_hom_action_ρ, CompHausLike.LocallyConstantModule.functor_obj_val, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesInjectiveObjects, FGModuleCat.FGModuleCatDual_obj, AlgebraicGeometry.tilde.functor_map, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, Rep.coindToInd_apply, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, SheafOfModules.pushforwardCongr_hom_app_val_app, hom_whiskerLeft, groupHomology.chainsMap_f_map_epi, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, groupHomology.mapCycles₂_comp, comp_apply, restrictScalarsCongr_hom_app, MonoidalCategory.tensorUnit_carrier, kernelIsoKer_inv_kernel_ι_apply, groupHomology.isoShortComplexH1_hom, ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.whiskering_linearYoneda, Rep.coe_of, MonoidalCategory.rightUnitor_hom_apply, groupCohomology.mono_map_0_of_mono, Condensed.instHasLimitsOfSizeModuleCat, groupCohomology.isoCocycles₂_hom_comp_i, CoalgCat.MonoidalCategory.inducingFunctorData_μIso, CoalgCat.MonoidalCategory.inducingFunctorData_εIso, FilteredColimits.M.mk_map, groupCohomology.π_comp_H0Iso_hom_apply, instIsRightAdjointRestrictScalars, Rep.resIndAdjunction_homEquiv_symm_apply, groupHomology.coe_mapCycles₂, Rep.coinvariantsFunctor_hom_ext_iff, LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim, CategoryTheory.whiskering_linearCoyoneda₂, FGModuleCat.obj_carrier, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, groupHomology.H1π_comp_map_apply, localizedModule_functor_map, Rep.instLinearModuleCatCoinvariantsFunctor, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', FGModuleCat.FGModuleCatCoevaluation_apply_one, Rep.coindMap'_hom, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₂, Rep.normNatTrans_app, groupHomology.H0π_comp_map_assoc, instHasExtModuleCatOfSmall, groupCohomology.dArrowIso₀₁_hom_left, instHasLimitsCondensedMod, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, groupCohomology.H1InfRes_X₃, MonoidalCategory.tensorLift_tmul, simple_of_isSimpleModule, Rep.applyAsHom_comm_assoc, MatrixModCat.toModuleCat_obj_carrier, Rep.instEpiModuleCatAppActionCoinvariantsMk, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, groupCohomology.cocycles₁_map_inv, Rep.freeLiftLEquiv_apply, hom_hom_leftUnitor, groupHomology.chainsFunctor_obj, groupCohomology.mapCocycles₁_one, Rep.instEnoughProjectives, PresheafOfModules.surjective_of_epi, groupCohomology.instMonoModuleCatFShortComplexH0, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, adj_homEquiv, groupCohomology.functor_obj, groupCohomology.cocyclesMap_comp, CategoryTheory.preservesFiniteColimits_preadditiveYonedaObj_of_injective, groupHomology.H2π_comp_map_assoc, AlgebraicGeometry.tilde.map_comp_assoc, Rep.indToCoindAux_mul_fst, hom_hom_rightUnitor, LightCondensed.forget_map_val_app, biprodIsoProd_inv_comp_snd, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, piIsoPi_inv_kernel_ι_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, Rep.ihom_obj_ρ_apply, Rep.instPreservesZeroMorphismsModuleCatInvariantsFunctor, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CondensedMod.hom_naturality_apply, instIsLeftAdjointRestrictScalars, lof_coprodIsoDirectSum_inv_apply, Condensed.instIsRightKanExtensionFintypeCatCondensedModProfiniteProfiniteSolidProfiniteSolidCounit, Rep.FiniteCyclicGroup.chainComplexFunctor_map_f, groupHomology.d₁₀ArrowIso_inv_right, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, Rep.finsuppTensorRight_hom_hom, QuadraticModuleCat.forget₂_map_associator_hom, exteriorPower.iso₀_hom_naturality_assoc, groupCohomology.resNatTrans_app, PresheafOfModules.injective_of_mono, free_ε_one, PresheafOfModules.isoMk_inv_app, groupCohomology.norm_ofAlgebraAutOnUnits_eq, groupCohomology.π_comp_H0Iso_hom_assoc, groupCohomology.π_map, CategoryTheory.full_linearCoyoneda, TannakaDuality.FiniteGroup.forget_map, MonModuleEquivalenceAlgebra.functor_obj_carrier, imageIsoRange_hom_subtype_assoc, groupCohomology.mem_cocycles₂_iff, groupCohomology.mapShortComplexH2_zero, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyonedaObj, Rep.tensor_ρ, Rep.resIndAdjunction_homEquiv_apply, Rep.toAdditive_apply, PresheafOfModules.pushforward_obj_map_apply, groupHomology.chainsMap_id_f_map_epi, groupCohomology.H2π_comp_map_assoc, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, AlgebraicGeometry.tilde.isIso_toOpen_top, groupHomology.mapCycles₂_comp_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, Rep.ofDistribMulAction_ρ_apply_apply, groupCohomology.d₀₁_ker_eq_invariants, Rep.linearization_η_hom_apply, CategoryTheory.faithful_linearCoyoneda, smulNatTrans_apply_app, FGModuleCat.ihom_obj, groupCohomology.cochainsMap_id_f_map_mono, CoalgCat.comonEquivalence_functor, Rep.quotientToInvariantsFunctor_map_hom, groupHomology.chainsMap_id_comp, forget_reflectsLimits, Rep.leftRegularHomEquiv_symm_apply, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, FDRep.char_linHom, Rep.quotientToCoinvariantsFunctor_map_hom, groupHomology.instEpiModuleCatGH1CoresCoinf, groupCohomology.mapShortComplexH1_id, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, Rep.coinvariantsShortComplex_g, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, reflectsIsomorphisms_extendScalars_of_faithfullyFlat, ExtendRestrictScalarsAdj.homEquiv_symm_apply, groupHomology.H1AddEquivOfIsTrivial_single, LightCondMod.instReflectsEpimorphismsLightCondSetForget, CategoryTheory.preservesFiniteColimits_preadditiveCoyonedaObj_of_projective, groupCohomology.mem_cocycles₁_iff, groupHomology.mapShortComplexH1_id_comp, CoalgCat.ofComonObjCoalgebraStruct_comul, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, groupHomology.mapShortComplexH1_comp, groupHomology.range_d₁₀_eq_coinvariantsKer, PresheafOfModules.unitHomEquiv_apply_coe, Rep.coindResAdjunction_homEquiv_apply, groupCohomology.inhomogeneousCochains.d_comp_d, FreeMonoidal.εIso_inv_freeMk, groupHomology.isoCycles₂_hom_comp_i_apply, Rep.Tor_map, Rep.ofModuleMonoidAlgebra_obj_ρ, PresheafOfModules.freeObj_obj, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, Rep.coinvariantsShortComplex_f, SheafOfModules.pushforwardCongr_inv_app_val_app, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, Rep.resIndAdjunction_counit_app, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles, groupHomology.π_comp_H0IsoOfIsTrivial_hom, RestrictionCoextensionAdj.unit'_app, matrixEquivalence_unitIso, groupHomology.eq_d₂₁_comp_inv_assoc, imageIsoRange_inv_image_ι, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom, Rep.ofMulActionSubsingletonIsoTrivial_inv_hom, smulShortComplex_X₃_carrier, RingCat.moduleCatRestrictScalarsPseudofunctor_mapId, free_η_freeMk, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, CategoryTheory.preservesHomology_preadditiveCoyonedaObj_of_projective, Rep.instIsLeftAdjointModuleCatCoinvariantsFunctor, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, Algebra.instLinearRestrictScalars, groupHomology.inhomogeneousChains.d_single, groupCohomology.coboundariesOfIsCoboundary₁_coe, groupCohomology.mapShortComplexH2_τ₁, FGModuleRepr.instIsEquivalenceFGModuleCatEmbed, groupHomology.cyclesIso₀_inv_comp_iCycles, instReflectsIsomorphismsRestrictScalars, exteriorPower.iso₁_hom_apply, FGModuleCat.instHasFiniteColimits, Representation.coind'_apply_apply, groupCohomology.d₁₂_comp_d₂₃_assoc, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, Rep.diagonalOneIsoLeftRegular_inv_hom, hom_inv_rightUnitor, ExtendScalars.smul_tmul, LightCondensed.free_internallyProjective_iff_tensor_condition', groupHomology.map_id_comp_H0Iso_hom_assoc, instHasLimitsOfSizeCondensedMod, hom_sum, MonModuleEquivalenceAlgebra.inverse_obj_mon, restrictScalarsComp'App_hom_naturality, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, groupCohomology.mapShortComplexH2_id_comp_assoc, groupHomology.mapCycles₂_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, Rep.coindIso_inv_hom_hom, hom_nsmul, groupHomology.mapShortComplexH2_comp, groupCohomology.map_id_comp_H0Iso_hom_apply, groupCohomology.cocycles₁_map_mul_of_isTrivial, forget_obj, directLimitDiagram_obj_isAddCommGroup, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.chainsMap_id_f_hom_eq_mapRange, CategoryTheory.preservesLimits_preadditiveYonedaObj, PresheafOfModules.toPresheaf_map_app_apply, groupHomology.toCycles_comp_isoCycles₂_hom, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupCohomology.map_id_comp_H0Iso_hom, CoalgCat.comonEquivalence_unitIso, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, PresheafOfModules.neg_app, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mapShortComplexH2_τ₂, groupHomology.mapCycles₁_id_comp, Rep.trivialFunctor_obj_V, Rep.indToCoindAux_mul_snd, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, homEquiv_extendScalarsComp, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, QuadraticModuleCat.toModuleCat_tensor, ExtendScalars.map_tmul, FilteredColimits.colimit_add_mk_eq', PresheafOfModules.map_comp, FilteredColimits.forget_reflectsFilteredColimits, RingCat.moduleCatRestrictScalarsPseudofunctor_map, groupCohomology.cocyclesOfIsMulCocycle₂_coe, groupHomology.chainsMap_f_map_mono, LinearMap.id_moduleCat_comp, restrictScalarsComp'App_inv_naturality, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, groupHomology.shortComplexH0_f, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.Iso.toLinearEquiv_apply, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, FDRep.instHasKernels, instHasZeroObject, PresheafOfModules.evaluation_preservesColimitsOfSize, groupHomology.isoShortComplexH1_inv, groupCohomology.coboundariesOfIsMulCoboundary₁_coe, SheafOfModules.pushforwardComp_hom_app_val_app, groupHomology.eq_d₁₀_comp_inv_assoc, groupCohomology.d₁₂_comp_d₂₃, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, Rep.linearization_obj_ρ, Rep.toCoinvariantsMkQ_hom, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, MonoidalCategory.tensorObj, restrictScalarsComp'App_inv_naturality_assoc, groupHomology.isoCycles₁_hom_comp_i_apply, LightCondMod.LocallyConstant.instIsIsoLightCondSetMapForgetAppLightCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, groupHomology.mapShortComplexH1_τ₁, PresheafOfModules.evaluation_preservesFiniteLimits, SheafOfModules.Presentation.map_relations_I, FGModuleCat.Iso.conj_eq_conj, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, hasCokernels_moduleCat, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, imageIsoRange_inv_image_ι_assoc, MonoidalCategory.rightUnitor_inv_apply, groupCohomology.H1π_eq_zero_iff, groupHomology.H1AddEquivOfIsTrivial_symm_apply, Rep.invariantsAdjunction_counit_app_hom, PresheafOfModules.sub_app, groupHomology.cyclesMap_comp_cyclesIso₀_hom, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, groupCohomology.coboundaries₁.val_eq_coe, groupHomology.d₃₂_single_one_fst, inhomogeneousCochains.d_hom_apply, Rep.coind'_ext_iff, CoalgCat.counit_def, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, groupHomology.chainsMap_comp, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, groupHomology.d₂₁_comp_d₁₀, PresheafOfModules.Elements.fromFreeYoneda_app_apply, binaryProductLimitCone_cone_π_app_left, HasColimit.coconePointSMul_apply, PresheafOfModules.pushforward_obj_obj, Rep.instLinearModuleCatInvariantsFunctor, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, kernelIsoKer_hom_ker_subtype, projective_of_categoryTheory_projective, smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, hasLimitsOfShape, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, hom_add, groupHomology.single_ρ_self_add_single_inv_mem_boundaries₁, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, Rep.ofMulActionSubsingletonIsoTrivial_hom_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_carrier, instEnoughInjectivesModuleCatOfSmall, groupCohomology.cocyclesMk₁_eq, AlgCat.forget₂_module_obj, isZero_groupCohomology_succ_of_subsingleton, MonoidalCategory.leftUnitor_inv_apply, groupCohomology.map_id_comp_assoc, ι_coprodIsoDirectSum_hom, instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, SheafOfModules.relationsOfIsCokernelFree_I, MonModuleEquivalenceAlgebra.algebraMap, MonoidalCategory.tensorμ_apply, Rep.linearizationTrivialIso_inv_hom, Rep.isZero_Tor_succ_of_projective, groupHomology.cyclesOfIsCycle₁_coe, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, groupCohomology.H1InfRes_X₁, Rep.quotientToInvariantsFunctor_obj_V, FDRep.char_one, groupHomology.shortComplexH0_exact, MonoidalCategory.tensorObj_isModule, groupHomology.inhomogeneousChains.ext_iff, FGModuleCat.hom_ext_iff, CategoryTheory.Abelian.FreydMitchell.instPreservesFiniteLimitsModuleCatEmbeddingRingFunctor, MonoidalCategory.tensorObj_isAddCommGroup, groupHomology.d₂₁_apply_mem_cycles₁, groupCohomology.coboundariesToCocycles₂_apply, ihom_map_apply, LightCondMod.LocallyConstant.instFaithfulModuleCatLightCondensedDiscrete, instAdditiveRestrictScalars, MonModuleEquivalenceAlgebra.inverseObj_mul, ihom_coev_app, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.cocyclesOfIsMulCocycle₁_coe, groupCohomology.H2π_eq_zero_iff, Rep.coinvariantsTensorIndNatIso_hom_app, groupHomology.π_map_assoc, PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation, groupHomology.congr, groupCohomology.mapCocycles₁_comp_i_assoc, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, Rep.applyAsHom_comm, groupCohomology.cocycles₁.val_eq_coe, instAdditiveUliftFunctor, TannakaDuality.FiniteGroup.sumSMulInv_single_id, PresheafOfModules.Hom.naturality_assoc, groupCohomology.H1π_comp_map_apply, Rep.leftRegularHom_hom_single, groupCohomology.cocycles₁_map_one, groupHomology.eq_d₃₂_comp_inv_assoc, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, hom_hom_associator, CoalgCat.forget₂_obj, groupCohomology.π_comp_H2Iso_hom_assoc, groupCohomology.H1InfRes_g, instHasLimitsOfSizeLightCondMod_1, CategoryTheory.preservesHomology_preadditiveYonedaObj_of_injective, CategoryTheory.linearCoyoneda_obj_map, Rep.standardComplex.d_comp_ε, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₃, FDRep.simple_iff_end_is_rank_one, Rep.finsuppTensorRight_inv_hom, matrixEquivalence_counitIso, Rep.coinvariantsMk_app_hom, Rep.ihom_obj_V_isAddCommGroup, CategoryTheory.linearYoneda_obj_additive, Rep.indCoindNatIso_inv_app, groupHomology.shortComplexH2_g, AddCommGrpCat.injective_as_module_iff, PresheafOfModules.restriction_app, groupCohomology.mapShortComplexH1_id_comp, PresheafOfModules.ι_fromFreeYonedaCoproduct_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, CategoryTheory.ShortComplex.moduleCat_exact_iff, groupCohomology.cocyclesMap_comp_assoc, groupHomology.mapCycles₂_hom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, mkOfSMul_smul, groupCohomology.instPreservesZeroMorphismsRepModuleCatFunctor, groupHomology.isoShortComplexH2_hom, Rep.coindResAdjunction_homEquiv_symm_apply, LightCondMod.LocallyConstant.instFaithfulModuleCatFunctor, instMonoι, restrictScalars.smul_def, kernelIsoKer_hom_ker_subtype_apply, exteriorPower.iso₁_hom_naturality_assoc, CategoryTheory.preadditiveYonedaObj_obj_isAddCommGroup, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, restrictScalarsId'_hom_app, Rep.coindVEquiv_apply_hom, groupCohomology.mapShortComplexH1_comp, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, groupHomology.H1π_eq_zero_iff, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, groupHomology.π_comp_H1Iso_hom_assoc, LightCondMod.hom_naturality_apply, PresheafOfModules.forgetToPresheafModuleCat_obj, groupHomology.chainsMap_f_2_comp_chainsIso₂, groupHomology.d₂₁_single_one_fst, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, HasLimit.productLimitCone_cone_pt_isModule, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, PresheafOfModules.forgetToPresheafModuleCatObj_obj, groupHomology.pOpcycles_comp_opcyclesIso_hom, groupHomology.H2π_comp_map, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Module.injective_iff_injective_object, groupCohomology.cocycles₂.val_eq_coe, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, groupHomology.π_comp_H2Iso_inv, groupCohomology.eq_d₂₃_comp_inv, instMonoidalLinear, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupCohomology.cochainsMap_f_map_mono, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_f, LightCondensed.ihomPoints_symm_apply, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, groupCohomology.isoShortComplexH1_hom, groupHomology.mapShortComplexH1_id, PresheafOfModules.Monoidal.tensorHom_app, instFaithfulUliftFunctor, groupHomology.H1π_comp_map_assoc, groupCohomology.map_id_comp, Rep.ihom_map_hom, groupHomology.instEpiModuleCatH1π, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, FGModuleCat.instHasLimitsOfShapeOfFinCategory, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, groupHomology.H1AddEquivOfIsTrivial_apply, MonoidalCategory.whiskerRight_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, Rep.finsuppTensorLeft_inv_hom, instPreservesLimitsOfSizeUliftFunctor, free_δ_freeMk, FGModuleCat.instFullUlift, forget₂AddCommGroup_reflectsLimitOfSize, PresheafOfModules.instMonoModuleCatCarrierObjOppositeRingCatApp, FilteredColimits.ι_colimitDesc, CoalgCat.forget₂_map, groupHomology.single_one_snd_sub_single_one_snd_mem_boundaries₂, Rep.unit_iso_comm, Rep.leftRegularHomEquiv_symm_single, restrictScalarsEquivalenceOfRingEquiv_additive, inhomogeneousCochains.d_eq, HasLimit.productLimitCone_cone_pt_carrier, groupHomology.instEpiModuleCatH2π, groupHomology.H1CoresCoinfOfTrivial_exact, MoritaEquivalence.instAdditiveModuleCatFunctorEqv, Rep.FiniteCyclicGroup.resolution_complex, piIsoPi_hom_ker_subtype, directLimitDiagram_obj_carrier, groupHomology.chainsFunctor_map, hom_id, groupCohomology.cocyclesMk₂_eq, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, Rep.leftRegularTensorTrivialIsoFree_inv_hom, extendScalars_id_comp_assoc, groupHomology.instPreservesZeroMorphismsRepChainComplexModuleCatNatChainsFunctor, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, AlgebraicGeometry.instFaithfulModuleCatCarrierModulesSpecOfFunctor, groupCohomology.cochainsMap_id_f_map_epi, instAB5ModuleCat, groupHomology.H1π_comp_map, groupHomology.chainsMap_f_hom, AlgCat.forget₂Module_preservesLimits, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles, groupHomology.d₃₂_apply_mem_cycles₂, MonoidalCategory.tensorUnit_isModule, extendScalars_assoc', piIsoPi_inv_kernel_ι, LightCondMod.LocallyConstant.instFullModuleCatFunctor, Rep.norm_hom, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.indResAdjunction_unit_app_hom_hom, CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj, Rep.ofHom_ρ, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, extendScalars_id_comp, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom, groupHomology.boundariesOfIsBoundary₂_coe, AlgebraicGeometry.tilde.map_add, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, groupHomology.cyclesMk₁_eq, groupHomology.H1CoresCoinfOfTrivial_f, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, groupHomology.cyclesIso₀_comp_H0π_assoc, Rep.coindFunctor'_obj, LightCondensed.ihom_map_val_app, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, wellPowered_moduleCat, FGModuleCat.tensorObj_obj, FGModuleCat.tensorUnit_obj, FreeMonoidal.μIso_inv_freeMk, uliftFunctor_map, Rep.Action_ρ_eq_ρ, Rep.linearization_δ_hom, groupHomology.functor_map, groupHomology.instEpiModuleCatH0π, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, groupCohomology.H1InfRes_exact, instPreservesFiniteLimitsUliftFunctor, MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, groupCohomology.mapShortComplexH2_τ₂, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, Rep.coindMap_hom, instHasFiniteLimitsLightCondMod, groupHomology.mapCycles₂_id_comp_apply, ChainComplex.linearYonedaObj_d, Rep.standardComplex.instQuasiIsoNatεToSingle₀, Rep.trivial_def, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, groupCohomology.cocycles₂_ext_iff, finite_ext, Rep.standardComplex.x_projective, ExtendRestrictScalarsAdj.counit_app, directLimitCocone_ι_app, AlgebraicGeometry.tilde.toOpen_res, AlgebraicGeometry.tilde.toOpen_res_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₁_isModule, FGModuleCat.instHasFiniteLimits, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.faithful_embedding, groupCohomology.instAdditiveRepCochainComplexModuleCatNatCochainsFunctor, instFiniteCarrierObjModuleCatIsFG, Rep.MonoidalClosed.linearHomEquiv_hom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, Rep.invariantsAdjunction_homEquiv_apply_hom, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, isZero_Ext_succ_of_projective, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, CategoryTheory.full_linearYoneda, CategoryTheory.Abelian.preadditiveCoyonedaObj_map_surjective, Rep.hom_comm_apply, SheafOfModules.pushforwardNatTrans_app_val_app, groupHomology.H2π_comp_map_apply, Hom.hom₂_apply, Rep.instPreservesEpimorphismsSubtypeMemSubgroupCoindFunctorSubtype, HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, Rep.FiniteCyclicGroup.resolution_quasiIso, uliftFunctor_obj, forget₂_addCommGrp_additive, Module.Flat.iff_preservesFiniteLimits_tensorLeft, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, groupCohomology.H1Map_id, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₁, groupCohomology.coboundaries₁_ext_iff, Rep.finsuppTensorLeft_hom_hom, Rep.indFunctor_map, groupHomology.H1CoresCoinfOfTrivial_g, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, instFaithfulRestrictScalars, MatrixModCat.toModuleCat_map, groupHomology.π_comp_H0Iso_hom, PresheafOfModules.map_id, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, MonoidalCategory.leftUnitor_def, groupCohomology.mapShortComplexH1_id_comp_assoc, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, groupCohomology.mapShortComplexH1_zero, binaryProductLimitCone_isLimit_lift, IsSMulRegular.smulShortComplex_shortExact, CategoryTheory.ShortComplex.moduleCatMk_f, homLinearEquiv_apply, groupCohomology.mapShortComplexH1_comp_assoc, Rep.coinvariantsTensorMk_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap, localizedModule_functor_obj, instHasLimitsOfSizeLightCondMod, instProjectiveObjFree, Rep.indMap_hom, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.Abelian.FreydMitchell.instPreservesFiniteColimitsModuleCatEmbeddingRingFunctor, groupHomology.isoCycles₁_hom_comp_i_assoc, Rep.coinvariantsShortComplex_X₁, Rep.homEquiv_symm_apply_hom, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, CategoryTheory.linearYoneda_obj_obj_isModule, AlgCat.forget₂_module_map, FilteredColimits.M.mk_surjective, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Rep.invariantsFunctor_map_hom, Iso.conj_eq_conj, instHasColimitsCondensedMod, groupHomology.map_id_comp_H0Iso_hom, groupCohomology.isoShortComplexH2_hom, linearEquivIsoModuleIso_inv, groupHomology.d₁₀_eq_zero_of_isTrivial, CoalgCat.toComon_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, groupCohomology.d₀₁_comp_d₁₂_assoc, groupCohomology.cocyclesMap_id, Rep.instIsRightAdjointActionModuleCatRes, MonoidalCategory.tensorObj_def, AlgebraicGeometry.tilde.map_zero, preservesFiniteLimits_tensorLeft_of_ringHomFlat, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVOfIsNoetherianRing, groupHomology.d₂₁_single_one_snd, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, Rep.norm_comm_assoc, groupCohomology.mapShortComplexH2_id_comp, groupHomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₃_isModule, FDRep.instFiniteCarrierVFGModuleCat, biprodIsoProd_inv_comp_fst, groupHomology.π_map_apply, CategoryTheory.Abelian.FreydMitchell.instFullModuleCatEmbeddingRingFunctor, Rep.resIndAdjunction_unit_app, instIsLeftAdjointExtendScalars, groupHomology.d₃₂_comp_d₂₁, groupHomology.d₃₂_single_one_snd, groupHomology.instEpiModuleCatGShortComplexH0, CategoryTheory.IsGrothendieckAbelian.instIsLeftAdjointModuleCatMulOppositeEndTensorObj, extendScalars_comp_id_assoc, instPreservesFiniteLimitsLocalizationLocalizedModule_functor, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, SheafOfModules.relationsOfIsCokernelFree_s, forget₂_reflectsLimits, FDRep.Iso.conj_ρ, FDRep.of_ρ, forget₂PreservesColimitsOfShape, CondensedMod.instHasLimitsOfSizeModuleCat, MatrixModCat.toModuleCat_obj_isAddCommGroup, Rep.diagonalOneIsoLeftRegular_hom_hom, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, Rep.ihom_coev_app_hom, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, Rep.leftRegularHomEquiv_apply, Rep.leftRegular_projective, CondensedMod.LocallyConstant.instFaithfulModuleCatFunctor, restrictScalars.smul_def', PresheafOfModules.pushforward_obj_map_apply', groupHomology.isoCycles₁_inv_comp_iCycles, groupHomology.chainsMap_zero, groupHomology.H1CoresCoinfOfTrivial_g_epi, Module.injective_object_of_injective_module, FDRep.char_dual, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, PresheafOfModules.Hom.naturality, groupHomology.mapShortComplexH2_id_comp, FGModuleCat.FGModuleCatEvaluation_apply', forget₂AddCommGroup_reflectsLimit, groupHomology.isoShortComplexH2_inv, groupHomology.coe_mapCycles₁, groupHomology.toCycles_comp_isoCycles₁_hom, HasLimit.productLimitCone_cone_pt_isAddCommGroup, hom_inv_leftUnitor, SheafOfModules.forgetToSheafModuleCat_map_val, groupCohomology.d₀₁_comp_d₁₂_apply, Module.Flat.instPreservesFiniteLimitsModuleCatTensorLeftOfCarrier, free_map_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, Representation.linHom.mem_invariants_iff_comm, groupHomology.mapCycles₂_comp_i_apply, binaryProductLimitCone_cone_pt, LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat, AlgebraicGeometry.tilde.functor_obj, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ofHom₂_hom_apply_hom, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, groupHomology.boundariesToCycles₂_apply, groupCohomology.subtype_comp_d₀₁, MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, groupHomology.cyclesOfIsCycle₂_coe, Rep.freeLift_hom, groupHomology.isoCycles₂_hom_comp_i, instPreservesInjectiveObjectsUliftFunctorOfSmall, AlgebraicGeometry.tilde.toOpen_map_app_assoc, groupHomology.π_comp_H1Iso_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.π_map_apply, Rep.indToCoindAux_snd_mul_inv, LightCondensed.instCountableAB4StarLightCondMod, hom_sub, localCohomology.hasColimitDiagram, CoalgCat.ofComonObjCoalgebraStruct_counit, groupCohomology.cocyclesMap_id_comp, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimits, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, Rep.res_obj_ρ, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, instHasLimitsOfSize, ofHom₂_compr₂, LightCondMod.LocallyConstant.instFullModuleCatLightCondensedDiscrete, extendScalars_comp_id, PresheafOfModules.freeYonedaEquiv_comp, forget₂AddCommGroup_preservesLimit, groupCohomology.coboundaries₁_le_cocycles₁, hasKernels_moduleCat, groupHomology.shortComplexH0_g, Rep.ihom_obj_V_isModule, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, FreeMonoidal.εIso_hom_one, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, groupCohomology.mapShortComplexH2_id, groupHomology.d₁₀ArrowIso_hom_right, groupCohomology.shortComplexH0_exact, Rep.freeLift_hom_single_single, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, groupHomology.single_one_mem_boundaries₁, mono_iff_ker_eq_bot, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, groupHomology.π_comp_H1Iso_inv_apply, groupHomology.cyclesIso₀_comp_H0π, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.isoCocycles₂_hom_comp_i_apply, extendRestrictScalarsAdj_unit_app_apply, instMonoidalPreadditive, groupHomology.H1CoresCoinfOfTrivial_X₃, Rep.diagonalHomEquiv_apply, AlgebraicGeometry.tilde.map_comp, groupHomology.d₂₁_single, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, SheafOfModules.Presentation.IsFinite.finite_relations, Rep.coinvariantsAdjunction_unit_app_hom, Rep.freeLiftLEquiv_symm_apply, groupHomology.inhomogeneousChains.d_eq, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, Rep.epi_iff_surjective, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, CategoryTheory.ShortComplex.moduleCatMk_X₂_carrier, groupCohomology.cochainsFunctor_map, groupCohomology.coboundaries₂_ext_iff, groupHomology.d₁₀_comp_coinvariantsMk_assoc, MonoidalCategory.whiskerLeft_apply, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, PresheafOfModules.Finite.evaluation_preservesFiniteColimits, Rep.indToCoindAux_of_not_rel, groupCohomology.cocyclesOfIsCocycle₂_coe, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, Rep.applyAsHom_hom, groupCohomology.shortComplexH2_g, forget_map, instIsGrothendieckAbelianModuleCat, Rep.coinvariantsShortComplex_X₂, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapId, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, groupCohomology.H1π_comp_map, groupHomology.single_inv_ρ_self_add_single_mem_boundaries₁, groupHomology.cyclesMap_comp, LightCondensed.internallyProjective_iff_tensor_condition', smulShortComplex_X₃_isModule, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, Rep.indResHomEquiv_apply_hom, MonModuleEquivalenceAlgebra.inverse_map_hom, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, hasLimit, CategoryTheory.preservesLimits_preadditiveCoyonedaObj, instPreservesProjectiveObjectsUliftFunctorOfSmall, groupHomology.epi_map_0_of_epi, groupHomology.mapShortComplexH1_τ₃, directLimitCocone_pt_isModule, instLinearUliftFunctor, CommRingCat.KaehlerDifferential.ext_iff, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, groupCohomology.cocyclesMk₀_eq, AlgebraicGeometry.tilde.map_neg, endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, directLimitDiagram_map, Rep.linearizationTrivialIso_hom_hom, ofHom_id, LightCondensed.instIsGrothendieckAbelianLightCondMod, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, groupHomology.single_mem_cycles₂_iff, Rep.instIsRightAdjointSubtypeMemSubgroupIndFunctorSubtype, groupCohomology.isoShortComplexH1_inv, image.fac, CategoryTheory.additive_coyonedaObj, groupHomology.boundaries₁_le_cycles₁, LightCondMod.isDiscrete_iff_isDiscrete_forget, mono_as_hom'_subtype, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, FilteredColimits.ι_colimitDesc_assoc, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, hasColimitsOfShape, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc, Rep.coinvariantsAdjunction_homEquiv_apply_hom, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, groupHomology.H1CoresCoinf_f, Rep.diagonalSuccIsoFree_hom_hom_single, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, hom_neg, Rep.ihom_obj_ρ, instInvertibleCarrierOutModuleCatValSkeleton, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, Rep.free_ext_iff, MonoidalCategory.whiskerRight_def, AlgebraicGeometry.isIso_fromTildeΓ_iff, FGModuleCat.instFaithfulUlift, Rep.instPreservesLimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, groupCohomology.cochainsMap_id_comp_assoc, preservesLimit_restrictScalars, groupCohomology.cocycles₁_ext_iff, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, groupCohomology.map_H0Iso_hom_f_assoc, ofHom_apply, CategoryTheory.ShortComplex.Exact.moduleCat_of_range_eq_ker, TannakaDuality.FiniteGroup.ofRightFDRep_hom, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, AlgebraicGeometry.tilde.map_id_assoc, simple_iff_isSimpleModule', Rep.instIsLeftAdjointIndFunctor, groupHomology.shortComplexH1_g, Rep.instPreservesZeroMorphismsModuleCatCoinvariantsFunctor, restrictScalarsCongr_inv_app, groupCohomology.eq_d₁₂_comp_inv_assoc, Representation.linHom.invariantsEquivRepHom_apply_hom, groupHomology.cyclesMap_id, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.preservesFiniteColimits_embedding, groupCohomology.H1InfRes_f, Rep.instAdditiveModuleCatInvariantsFunctor, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, FGModuleCat.Iso.conj_hom_eq_conj, smulShortComplex_X₂, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, instFreeCarrierX₂ModuleCatProjectiveShortComplex, forget₂AddCommGroupIsEquivalence, Rep.barComplex.d_comp_diagonalSuccIsoFree_inv_eq, groupHomology.d₁₀ArrowIso_inv_left, monoidalClosed_pre_app, SheafOfModules.forgetToSheafModuleCat_obj_val, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, Rep.coindFunctor'_map, groupHomology.single_mem_cycles₁_iff, Rep.coinvariantsFunctor_map_hom, Rep.coindFunctor_obj, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π, groupHomology.d₂₁_single_ρ_add_single_inv_mul, PresheafOfModules.evaluation_obj, groupCohomology.mapShortComplexH2_τ₃, LinearEquiv.toModuleIso_hom, HasLimit.productLimitCone_isLimit_lift, MonoidalCategory.tensorObj_carrier, Rep.linearization_map_hom_single, isZero_groupHomology_succ_of_subsingleton, groupCohomology.isoShortComplexH2_inv, Algebra.restrictScalarsEquivalenceOfRingEquiv_linear, CategoryTheory.preadditiveCoyoneda_obj, groupCohomology.map_id_comp_H0Iso_hom_assoc, groupCohomology.isoCocycles₂_hom_comp_i_assoc, Rep.ihom_obj_ρ_def, groupHomology.eq_d₁₀_comp_inv_apply, Rep.ihom_obj_V_carrier, LinearEquiv.toFGModuleCatIso_inv, semilinearMapAddEquiv_apply, CoextendScalars.map'_hom_apply_apply, Rep.coinvariantsShortComplex_X₃, Rep.coindIso_hom_hom_hom, TannakaDuality.FiniteGroup.equivHom_surjective, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, freeHomEquiv_symm_apply, ulift_injective_of_injective, Rep.leftRegularTensorTrivialIsoFree_hom_hom, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, TannakaDuality.FiniteGroup.equivHom_injective, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, groupHomology.H0π_comp_H0Iso_hom_apply, Rep.barComplex.d_single, freeDesc_apply, groupHomology.mapShortComplexH2_τ₃, FDRep.hom_action_ρ, Rep.mono_iff_injective, MonoidalCategory.tensorUnit_isAddCommGroup, PresheafOfModules.evaluation_map, CategoryTheory.linearCoyoneda_obj_obj_isModule, FDRep.dualTensorIsoLinHom_hom_hom, homEquiv_extendScalarsId, ExtendScalars.hom_ext_iff, Rep.instMonoModuleCatHom, groupHomology.d₂₁_comp_d₁₀_assoc, groupCohomology.coe_mapCocycles₂, groupCohomology.eq_d₀₁_comp_inv_assoc, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, toKernelSubobject_arrow, groupCohomology.functor_map, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, CategoryTheory.Iso.toLinearMap_toLinearEquiv, instHasBinaryBiproducts, Rep.linearization_ε_hom, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, smulShortComplex_g_epi, Rep.Tor_obj, groupCohomology.isoCocycles₁_hom_comp_i_assoc, Rep.coinvariantsShortComplex_shortExact, groupHomology.π_comp_H1Iso_inv_assoc, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, Rep.FiniteCyclicGroup.resolution_π, Rep.instPreservesColimitsModuleCatForget₂HomSubtypeLinearMapIdCarrierV, groupHomology.mapCycles₁_quotientGroupMk'_epi, PresheafOfModules.zero_app, groupHomology.π_map, groupHomology.mapCycles₁_comp_i_assoc, groupHomology.H0π_comp_map_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc, PresheafOfModules.map_comp_assoc, restrictScalarsId'App_inv_apply, groupCohomology.mapShortComplexH1_τ₁, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, Rep.coinvariantsTensorFreeToFinsupp_mk_tmul_single, smulShortComplex_exact, groupHomology.π_comp_H2Iso_inv_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGV, groupCohomology.coboundariesOfIsCoboundary₂_coe, Rep.FiniteCyclicGroup.resolution.π_f, CoalgCat.toComon_obj, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, Rep.instAdditiveModuleCatCoinvariantsFunctor, PresheafOfModules.forgetToPresheafModuleCat_map, MonModuleEquivalenceAlgebra.inverseObj_one, groupCohomology.cochainsFunctor_obj, restrictScalarsComp'App_inv_apply, FDRep.endRingEquiv_comp_ρ, Rep.linearization_map_hom, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mem_cycles₁_iff, isZero_of_subsingleton, isZero_of_iff_subsingleton, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i, groupHomology.boundariesToCycles₁_apply, groupHomology.single_mem_cycles₂_iff_inv, groupHomology.d₁₀_single, SheafOfModules.Finite.evaluationPreservesFiniteLimits, CategoryTheory.IsGrothendieckAbelian.instIsRightAdjointModuleCatMulOppositeEndPreadditiveCoyonedaObj, instHasCoequalizers, exteriorPower.functor_obj, TannakaDuality.FiniteGroup.equivHom_apply, ihom_ev_app, groupCohomology.cocycles₁.d₁₂_apply, FDRep.simple_iff_char_is_norm_one, Rep.indResHomEquiv_symm_apply_hom, groupHomology.isoCycles₂_hom_comp_i_assoc, FilteredColimits.colimit_add_mk_eq, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, free_hom_ext_iff, groupHomology.chainsMap_f_0_comp_chainsIso₀, groupHomology.H2π_eq_zero_iff, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.ShortComplex.moduleCatMk_X₂_isAddCommGroup, LightCondensed.instIsMonoidalFunctorOppositeLightProfiniteModuleCatWCoherentTopology, enoughInjectives, FGModuleCat.instIsMonoidalModuleCatIsFG, extendScalars_assoc, MonoidalCategory.associator_inv_apply, preservesColimit_restrictScalars, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, isSeparator, instHasFiniteBiproducts, Rep.norm_comm, exteriorPower.functor_map, instEnoughInjectivesModuleCatInt, Rep.linearization_μ_hom, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.H1π_eq_iff, ExtendRestrictScalarsAdj.unit_app, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, FGModuleCat.instIsIsoCoimageImageComparison, CoextendScalars.map_apply, groupCohomology.shortComplexH1_g, groupHomology.chainsMap_f, Rep.quotientToCoinvariantsFunctor_obj_V, SheafOfModules.unitHomEquiv_apply_coe, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.preservesFiniteLimits_embedding, Profinite.NobelingProof.succ_mono, CategoryTheory.preadditiveYonedaObj_map, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, groupCohomology.map_comp_assoc, groupHomology.cyclesMap_comp_isoCycles₁_hom, groupCohomology.cochainsMap_id, forget₂_map, AlgebraicGeometry.tilde.toOpen_map_app, groupCohomology.d₀₁_eq_zero, Rep.instInjective, ChainComplex.linearYonedaObj_X, toMatrixModCat_obj_isModule
of 📖	CompOp	428 math math: CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, groupCohomology.instEpiModuleCatH2π, groupHomology.π_comp_H2Iso_hom_assoc, of_coe, biproductIsoPi_inv_comp_π, groupHomology.mapCycles₂_comp_assoc, groupCohomology.toCocycles_comp_isoCocycles₁_hom, CategoryTheory.linearCoyoneda_map_app, groupCohomology.isoCocycles₁_hom_comp_i_apply, groupCohomology.d₂₃_hom_apply, groupHomology.d₁₀_single_one, groupCohomology.d₀₁_comp_d₁₂, epi_as_hom''_mkQ, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, groupCohomology.cocyclesIso₀_hom_comp_f, Rep.resCoindAdjunction_counit_app_hom_hom, groupHomology.d₃₂_single, groupCohomology.eq_d₀₁_comp_inv, extendScalarsId_hom_app_one_tmul, groupCohomology.H1π_comp_map_assoc, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, groupCohomology.π_comp_H0Iso_hom, ofHom_comp, groupCohomology.π_comp_H1Iso_hom_assoc, ι_coprodIsoDirectSum_hom_apply, groupCohomology.eq_d₁₂_comp_inv, cokernel_π_cokernelIsoRangeQuotient_hom_apply, groupCohomology.mapCocycles₂_comp_i, groupHomology.eq_d₃₂_comp_inv, groupCohomology.H0IsoOfIsTrivial_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, CoextendScalars.smul_apply', groupHomology.cyclesMap_comp_isoCycles₂_hom, groupCohomology.d₁₂_hom_apply, groupHomology.comp_d₂₁_eq, groupHomology.mapCycles₁_comp_assoc, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, linearEquivIsoModuleIso_hom, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, groupCohomology.comp_d₁₂_eq, groupCohomology.cocycles₂.d₂₃_apply, groupCohomology.d₀₁_hom_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, groupHomology.isoCycles₁_inv_comp_iCycles_apply, groupCohomology.dArrowIso₀₁_inv_right, groupCohomology.map_H0Iso_hom_f_apply, groupCohomology.d₁₂_comp_d₂₃_apply, groupCohomology.H0IsoOfIsTrivial_inv_apply, groupCohomology.eq_d₂₃_comp_inv_assoc, groupCohomology.eq_d₂₃_comp_inv_apply, groupCohomology.eq_d₁₂_comp_inv_apply, groupHomology.chains₁ToCoinvariantsKer_surjective, Rep.coinvariantsTensorFreeLEquiv_symm_apply, LinearEquiv.toModuleIso_inv, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, exteriorPower.iso₀_hom_naturality, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Rep.resCoindAdjunction_unit_app_hom_hom, groupHomology.d₃₂_comp_d₂₁_assoc, endRingEquiv_symm_apply_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasLimit.productLimitCone_cone_π, CoalgCat.moduleCat_of_toModuleCat, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, groupHomology.d₂₁_single_inv_mul_ρ_add_single, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, groupCohomology.H1IsoOfIsTrivial_inv_apply, biprodIsoProd_inv_comp_snd_apply, RestrictionCoextensionAdj.counit'_app, groupHomology.chainsMap_f_3_comp_chainsIso₃, groupHomology.mapCycles₁_id_comp_assoc, groupHomology.eq_d₂₁_comp_inv, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, groupCohomology.H2π_comp_map_apply, groupHomology.mapCycles₁_comp, Profinite.NobelingProof.succ_exact, groupCohomology.dArrowIso₀₁_hom_right, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, groupCohomology.toCocycles_comp_isoCocycles₂_hom, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, imageIsoRange_hom_subtype, groupHomology.mapCycles₁_comp_i, CoextendScalars.smul_apply, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, imageIsoRange_inv_image_ι_apply, groupCohomology.comp_d₂₃_eq, cokernel_π_cokernelIsoRangeQuotient_hom, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupCohomology.d₁₂_apply_mem_cocycles₂, groupHomology.mapCycles₂_id_comp, groupCohomology.d₀₁_apply_mem_cocycles₁, exteriorPower.iso₀_hom_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupCohomology.subtype_comp_d₀₁_apply, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.comp_d₀₁_eq, homAddEquiv_symm_apply_hom, groupHomology.toCycles_comp_isoCycles₁_hom_apply, groupHomology.mapCycles₂_comp_i, groupCohomology.map_H0Iso_hom_f, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, groupHomology.eq_d₃₂_comp_inv_apply, lof_coprodIsoDirectSum_inv, CategoryTheory.linearYoneda_map_app, CoalgCat.comul_def, groupHomology.mapCycles₁_id_comp_apply, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_assoc, simple_iff_isSimpleModule, groupCohomology.instEpiModuleCatH1π, IsProjective.iff_projective, groupCohomology.H2π_comp_map, groupHomology.π_comp_H2Iso_hom, Rep.indResAdjunction_counit_app_hom_hom, FGModuleCat.FGModuleCatDual_obj, groupHomology.pOpcycles_comp_opcyclesIso_hom_apply, groupHomology.mapCycles₁_comp_i_apply, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, groupHomology.mapCycles₂_comp, kernelIsoKer_inv_kernel_ι_apply, ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, groupCohomology.isoCocycles₂_hom_comp_i, groupCohomology.π_comp_H0Iso_hom_apply, groupHomology.coe_mapCycles₂, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, groupHomology.H1π_comp_map_apply, groupCohomology.dArrowIso₀₁_hom_left, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, simple_of_isSimpleModule, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, groupCohomology.mapCocycles₁_one, groupHomology.H2π_comp_map_assoc, biprodIsoProd_inv_comp_snd, piIsoPi_inv_kernel_ι_apply, lof_coprodIsoDirectSum_inv_apply, groupHomology.d₁₀ArrowIso_inv_right, range_mkQ_cokernelIsoRangeQuotient_inv, exteriorPower.iso₀_hom_naturality_assoc, groupCohomology.π_comp_H0Iso_hom_assoc, imageIsoRange_hom_subtype_assoc, groupCohomology.H2π_comp_map_assoc, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, groupHomology.mapCycles₂_comp_apply, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, groupCohomology.d₀₁_ker_eq_invariants, groupHomology.H2π_eq_iff, groupHomology.H1AddEquivOfIsTrivial_single, groupHomology.range_d₁₀_eq_coinvariantsKer, groupCohomology.inhomogeneousCochains.d_comp_d, groupHomology.isoCycles₂_hom_comp_i_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assoc, groupCohomology.isoCocycles₁_inv_comp_iCocycles, RestrictionCoextensionAdj.unit'_app, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierOfCarrierStalkAbPresheafPrimeComplAsIdealHomToStalk, groupHomology.eq_d₂₁_comp_inv_assoc, imageIsoRange_inv_image_ι, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_apply, groupHomology.cyclesMap_comp_isoCycles₂_hom_assoc, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom, groupHomology.inhomogeneousChains.d_single, groupCohomology.d₁₂_comp_d₂₃_assoc, ExtendScalars.smul_tmul, QuadraticModuleCat.forget₂_obj, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, groupHomology.mapCycles₂_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, groupCohomology.map_id_comp_H0Iso_hom_apply, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.toCycles_comp_isoCycles₂_hom, groupCohomology.map_id_comp_H0Iso_hom, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, groupHomology.mapCycles₁_id_comp, coe_of, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, ExtendScalars.map_tmul, forget₂_obj_moduleCat_of, groupHomology.eq_d₁₀_comp_inv, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, groupHomology.isoShortComplexH1_inv, groupHomology.eq_d₁₀_comp_inv_assoc, groupCohomology.d₁₂_comp_d₂₃, groupHomology.chainsMap_f_1_comp_chainsIso₁_assoc, groupHomology.isoCycles₁_hom_comp_i_apply, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, imageIsoRange_inv_image_ι_assoc, groupCohomology.H1π_eq_zero_iff, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, groupHomology.d₃₂_single_one_fst, inhomogeneousCochains.d_hom_apply, CoalgCat.counit_def, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom_apply, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, groupHomology.d₂₁_comp_d₁₀, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, kernelIsoKer_hom_ker_subtype, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, groupHomology.H1ToTensorOfIsTrivial_H1π_single, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, groupCohomology.cocyclesMk₁_eq, AlgCat.forget₂_module_obj, ι_coprodIsoDirectSum_hom, Rep.quotientToInvariantsFunctor_obj_V, groupHomology.inhomogeneousChains.ext_iff, groupHomology.d₂₁_apply_mem_cycles₁, MonModuleEquivalenceAlgebra.inverseObj_mul, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom_apply, groupHomology.toCycles_comp_isoCycles₂_hom_apply, groupCohomology.H2π_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i_assoc, groupCohomology.H1π_comp_map_apply, groupHomology.eq_d₃₂_comp_inv_assoc, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, CoalgCat.forget₂_obj, groupCohomology.π_comp_H2Iso_hom_assoc, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, Rep.coinvariantsMk_app_hom, AddCommGrpCat.injective_as_module_iff, groupHomology.mapCycles₂_hom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, kernelIsoKer_hom_ker_subtype_apply, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, groupHomology.H1π_eq_zero_iff, groupHomology.isoCycles₁_inv_comp_iCycles_assoc, groupHomology.π_comp_H1Iso_hom_assoc, groupHomology.chainsMap_f_2_comp_chainsIso₂, groupHomology.d₂₁_single_one_fst, groupHomology.H2π_comp_map, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Module.injective_iff_injective_object, groupCohomology.eq_d₂₃_comp_inv, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupHomology.H1π_comp_map_assoc, groupHomology.instEpiModuleCatH1π, piIsoPi_hom_ker_subtype_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, inhomogeneousCochains.d_eq, groupHomology.instEpiModuleCatH2π, piIsoPi_hom_ker_subtype, groupCohomology.cocyclesMk₂_eq, groupHomology.H1π_comp_map, groupHomology.chainsMap_f_hom, groupHomology.d₃₂_apply_mem_cycles₂, piIsoPi_inv_kernel_ι, Rep.indResAdjunction_unit_app_hom_hom, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.cyclesMk₁_eq, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, groupCohomology.mapCocycles₁_comp_i_apply, groupHomology.mapCycles₂_id_comp_apply, directLimitCocone_ι_app, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, groupHomology.H2π_comp_map_apply, Hom.hom₂_apply, uliftFunctor_obj, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, binaryProductLimitCone_isLimit_lift, groupHomology.isoCycles₁_hom_comp_i_assoc, extendScalarsComp_hom_app_one_tmul, Rep.invariantsFunctor_map_hom, linearEquivIsoModuleIso_inv, groupHomology.d₁₀_eq_zero_of_isTrivial, groupCohomology.π_comp_H1Iso_hom_apply, groupCohomology.d₀₁_comp_d₁₂_assoc, preservesFiniteLimits_tensorLeft_of_ringHomFlat, groupHomology.d₂₁_single_one_snd, biprodIsoProd_inv_comp_fst, groupHomology.d₃₂_comp_d₂₁, groupHomology.d₃₂_single_one_snd, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, FDRep.of_ρ, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, groupHomology.isoCycles₁_inv_comp_iCycles, Module.injective_object_of_injective_module, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, FGModuleCat.FGModuleCatEvaluation_apply', groupHomology.isoShortComplexH2_inv, groupHomology.coe_mapCycles₁, groupHomology.toCycles_comp_isoCycles₁_hom, groupCohomology.d₀₁_comp_d₁₂_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, groupHomology.mapCycles₂_comp_i_apply, binaryProductLimitCone_cone_pt, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ofHom₂_hom_apply_hom, groupCohomology.subtype_comp_d₀₁, groupHomology.isoCycles₂_hom_comp_i, groupHomology.π_comp_H1Iso_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, groupHomology.isoCycles₂_inv_comp_iCycles, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, ofHom₂_compr₂, groupHomology.d₁₀ArrowIso_hom_right, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, groupHomology.π_comp_H1Iso_inv_apply, groupCohomology.isoCocycles₂_hom_comp_i_apply, groupHomology.d₂₁_single, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, hom_ofHom, groupHomology.inhomogeneousChains.d_eq, groupHomology.cycles₁IsoOfIsTrivial_inv_apply, groupHomology.eq_d₂₁_comp_inv_apply, groupHomology.d₁₀_comp_coinvariantsMk_assoc, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupCohomology.H1π_comp_map, MonModuleEquivalenceAlgebra.inverse_map_hom, PresheafOfModules.ofPresheaf_map, groupCohomology.cocyclesMk₀_eq, groupHomology.lsingle_comp_chainsMap_f_assoc, ofHom_id, groupCohomology.isoShortComplexH1_inv, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, sMulCommClass_mk, QuadraticModuleCat.moduleCat_of_toModuleCat, Rep.ihom_obj_ρ, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, groupCohomology.map_H0Iso_hom_f_assoc, ofHom_apply, kernelIsoKer_inv_kernel_ι, groupCohomology.eq_d₁₂_comp_inv_assoc, imageIsoRange_hom_subtype_apply, groupHomology.d₁₀ArrowIso_inv_left, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, Rep.coinvariantsFunctor_map_hom, groupHomology.d₂₁_single_ρ_add_single_inv_mul, LinearEquiv.toModuleIso_hom, HasLimit.productLimitCone_isLimit_lift, groupCohomology.isoShortComplexH2_inv, groupCohomology.map_id_comp_H0Iso_hom_assoc, groupCohomology.isoCocycles₂_hom_comp_i_assoc, groupHomology.eq_d₁₀_comp_inv_apply, CoextendScalars.map'_hom_apply_apply, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, ulift_injective_of_injective, ExtendScalars.hom_ext_iff, groupHomology.d₂₁_comp_d₁₀_assoc, groupCohomology.coe_mapCocycles₂, groupCohomology.eq_d₀₁_comp_inv_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, groupCohomology.isoCocycles₁_hom_comp_i_assoc, groupHomology.mapCycles₁_quotientGroupMk'_epi, groupHomology.mapCycles₁_comp_i_assoc, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, groupHomology.π_comp_H2Iso_inv_apply, MonModuleEquivalenceAlgebra.inverseObj_one, isZero_of_iff_subsingleton, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i, groupHomology.d₁₀_single, groupCohomology.cocycles₁.d₁₂_apply, groupHomology.isoCycles₂_hom_comp_i_assoc, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, groupHomology.H2π_eq_zero_iff, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, isSeparator, groupHomology.H1π_eq_iff, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, CoextendScalars.map_apply, groupHomology.chainsMap_f, Rep.quotientToCoinvariantsFunctor_obj_V, Profinite.NobelingProof.succ_mono, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom, groupCohomology.d₀₁_eq_zero
ofHom 📖	CompOp	130 math math: Rep.resCoindHomEquiv_symm_apply_hom, Rep.resCoindHomEquiv_apply_hom, CategoryTheory.preadditiveCoyonedaObj_map, biproductIsoPi_inv_comp_π, CategoryTheory.linearCoyoneda_map_app, Rep.MonoidalClosed.linearHomEquiv_symm_hom, epi_as_hom''_mkQ, toMatrixModCat_map, Rep.leftRegularHom_hom, ofHom_comp, CategoryTheory.linearYoneda_obj_map, CategoryTheory.ShortComplex.moduleCatMk_g, PresheafOfModules.restrictScalarsObj_map, Rep.standardComplex.d_eq, LinearEquiv.toModuleIso_inv, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Rep.homEquiv_apply_hom, HasLimit.productLimitCone_cone_π, QuadraticModuleCat.forget₂_map, RestrictionCoextensionAdj.counit'_app, MonoidalCategory.whiskerLeft_def, Rep.ihom_ev_app_hom, Profinite.NobelingProof.succ_exact, Rep.MonoidalClosed.linearHomEquivComm_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, imageIsoRange_hom_subtype, groupCohomology.shortComplexH0_f, binaryProductLimitCone_cone_π_app_right, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, MonoidalCategory.tensorHom_def, Rep.subtype_hom, cokernel_π_cokernelIsoRangeQuotient_hom, Rep.invariantsAdjunction_unit_app, lof_coprodIsoDirectSum_inv, CategoryTheory.linearYoneda_map_app, CoalgCat.comul_def, directLimitIsColimit_desc, smulShortComplex_g, Rep.coindMap'_hom, biprodIsoProd_inv_comp_snd, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, Rep.finsuppTensorRight_hom_hom, imageIsoRange_hom_subtype_assoc, TannakaDuality.FiniteGroup.equivApp_hom, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, RestrictionCoextensionAdj.unit'_app, imageIsoRange_inv_image_ι, Rep.ofMulActionSubsingletonIsoTrivial_inv_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, Rep.diagonalOneIsoLeftRegular_inv_hom, PresheafOfModules.homMk_app, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.lsingle_comp_chainsMap_f, imageIsoRange_inv_image_ι_assoc, Rep.invariantsAdjunction_counit_app_hom, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, CoalgCat.counit_def, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, binaryProductLimitCone_cone_π_app_left, kernelIsoKer_hom_ker_subtype, smulShortComplex_f, Rep.ofMulActionSubsingletonIsoTrivial_hom_hom, ι_coprodIsoDirectSum_hom, groupHomology.inhomogeneousChains.ext_iff, MonModuleEquivalenceAlgebra.inverseObj_mul, CategoryTheory.linearCoyoneda_obj_map, Rep.finsuppTensorRight_inv_hom, Rep.coindVEquiv_apply_hom, Rep.ihom_map_hom, Rep.finsuppTensorLeft_inv_hom, CoalgCat.forget₂_map, piIsoPi_hom_ker_subtype, Rep.leftRegularTensorTrivialIsoFree_inv_hom, piIsoPi_inv_kernel_ι, Rep.norm_hom, Rep.ofHom_ρ, uliftFunctor_map, Rep.linearization_δ_hom, ofHom_hom, Rep.coindMap_hom, ChainComplex.linearYonedaObj_d, directLimitCocone_ι_app, Rep.MonoidalClosed.linearHomEquiv_hom, Hom.hom₂_apply, Rep.finsuppTensorLeft_hom_hom, MatrixModCat.toModuleCat_map, binaryProductLimitCone_isLimit_lift, CategoryTheory.ShortComplex.moduleCatMk_f, Rep.indMap_hom, Rep.homEquiv_symm_apply_hom, AlgCat.forget₂_module_map, CoalgCat.toComon_map_hom, biprodIsoProd_inv_comp_fst, Rep.diagonalOneIsoLeftRegular_hom_hom, Rep.ihom_coev_app_hom, groupCohomology.subtype_comp_d₀₁, Rep.freeLift_hom, ofHom₂_compr₂, hom_ofHom, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, Rep.applyAsHom_hom, Rep.indResHomEquiv_apply_hom, MonModuleEquivalenceAlgebra.inverse_map_hom, PresheafOfModules.ofPresheaf_map, groupHomology.lsingle_comp_chainsMap_f_assoc, directLimitDiagram_map, ofHom_id, mono_as_hom'_subtype, MonoidalCategory.whiskerRight_def, ofHom_apply, TannakaDuality.FiniteGroup.ofRightFDRep_hom, kernelIsoKer_inv_kernel_ι, Representation.linHom.invariantsEquivRepHom_apply_hom, Rep.mkQ_hom, monoidalClosed_pre_app, LinearEquiv.toModuleIso_hom, HasLimit.productLimitCone_isLimit_lift, semilinearMapAddEquiv_apply, Rep.leftRegularTensorTrivialIsoFree_hom_hom, Rep.linearization_ε_hom, MonModuleEquivalenceAlgebra.inverseObj_one, Rep.linearization_map_hom, ihom_ev_app, Rep.indResHomEquiv_symm_apply_hom, Rep.linearization_μ_hom, groupHomology.chainsMap_f, Profinite.NobelingProof.succ_mono, CategoryTheory.preadditiveYonedaObj_map
ofHom₂ 📖	CompOp	5 math math: ofHom₂_hom₂, ihom_coev_app, ofHom₂_hom_apply_hom, ofHom₂_compr₂, Hom.hom₂_ofHom₂
smul 📖	CompOp	4 math math: smul_naturality, smulNatTrans_apply_app, HasColimit.coconePointSMul_apply, mkOfSMul_smul
smulNatTrans 📖	CompOp	1 math math: smulNatTrans_apply_app
«term↟_» 📖	CompOp	—

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe_of 📖	mathematical	—	carrier of Ring.toAddCommGroup	—	—
comp_apply 📖	mathematical	—	DFunLike.coe carrier CategoryTheory.ConcreteCategory.hom ModuleCat moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier CategoryTheory.CategoryStruct.comp CategoryTheory.Category.toCategoryStruct	—	—
endRingEquiv_apply 📖	mathematical	—	DFunLike.coe RingEquiv CategoryTheory.End ModuleCat CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule CategoryTheory.End.mul Module.End.instMul Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing CategoryTheory.Preadditive.instRingEnd instPreadditive LinearMap.instAdd EquivLike.toFunLike RingEquiv.instEquivLike endRingEquiv Hom.hom	—	—
endRingEquiv_symm_apply_hom 📖	mathematical	—	Hom.hom of carrier isAddCommGroup isModule DFunLike.coe RingEquiv LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid CategoryTheory.End ModuleCat CategoryTheory.Category.toCategoryStruct moduleCategory Module.End.instMul CategoryTheory.End.mul LinearMap.instAdd Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonAssocRing.toNonUnitalNonAssocRing Ring.toNonAssocRing CategoryTheory.Preadditive.instRingEnd instPreadditive EquivLike.toFunLike RingEquiv.instEquivLike RingEquiv.symm endRingEquiv	—	—
forget_map 📖	mathematical	—	CategoryTheory.Functor.map ModuleCat moduleCategory CategoryTheory.types CategoryTheory.forget LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier DFunLike.coe CategoryTheory.ConcreteCategory.hom	—	—
forget_obj 📖	mathematical	—	CategoryTheory.Functor.obj ModuleCat moduleCategory CategoryTheory.types CategoryTheory.forget LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier	—	—
forget₂_addCommGrp_additive 📖	mathematical	—	CategoryTheory.Functor.Additive ModuleCat AddCommGrpCat moduleCategory AddCommGrpCat.instCategory instPreadditive AddCommGrpCat.instPreadditive CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup	—	—
forget₂_map 📖	mathematical	—	CategoryTheory.Functor.map ModuleCat moduleCategory AddCommGrpCat AddCommGrpCat.instCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup AddCommGrpCat.ofHom AddMonoidHomClass.toAddMonoidHom DistribMulActionSemiHomClass.toAddMonoidHomClass DFunLike.coe RingHom RingHom.instFunLike MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction SemilinearMapClass.distribMulActionSemiHomClass LinearMap.semilinearMapClass Hom.hom	—	—
forget₂_map_homMk 📖	mathematical	CategoryTheory.CategoryStruct.comp AddCommGrpCat CategoryTheory.Category.toCategoryStruct AddCommGrpCat.instCategory CategoryTheory.Functor.obj ModuleCat moduleCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup DFunLike.coe RingHom CategoryTheory.End CategoryTheory.Preadditive.instSemiringEnd AddCommGrpCat.instPreadditive RingHom.instFunLike smul	CategoryTheory.Functor.map homMk	—	—
forget₂_obj 📖	mathematical	—	CategoryTheory.Functor.obj ModuleCat moduleCategory AddCommGrpCat AddCommGrpCat.instCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup AddCommGrpCat.of	—	—
forget₂_obj_moduleCat_of 📖	mathematical	—	CategoryTheory.Functor.obj ModuleCat moduleCategory AddCommGrpCat AddCommGrpCat.instCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup of AddCommGrpCat.of	—	—
homAddEquiv_apply 📖	mathematical	—	DFunLike.coe AddEquiv Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule instAddHom LinearMap.instAdd EquivLike.toFunLike AddEquiv.instEquivLike homAddEquiv Hom.hom	—	—
homAddEquiv_symm_apply_hom 📖	mathematical	—	Hom.hom of carrier isAddCommGroup isModule DFunLike.coe AddEquiv LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap.instAdd instAddHom EquivLike.toFunLike AddEquiv.instEquivLike AddEquiv.symm homAddEquiv	—	—
homLinearEquiv_apply 📖	mathematical	—	DFunLike.coe LinearEquiv RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap Ring.toSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule instAddCommGroupHom LinearMap.addCommMonoid Hom.instModule LinearMap.module EquivLike.toFunLike LinearEquiv.instEquivLike homLinearEquiv Equiv.toFun AddEquiv.toEquiv instAddHom LinearMap.instAdd homAddEquiv	—	RingHomInvPair.ids
homLinearEquiv_symm_apply 📖	mathematical	—	DFunLike.coe LinearEquiv RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids LinearMap Ring.toSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap.addCommMonoid instAddCommGroupHom LinearMap.module Hom.instModule EquivLike.toFunLike LinearEquiv.instEquivLike LinearEquiv.symm homLinearEquiv Equiv.invFun AddEquiv.toEquiv instAddHom LinearMap.instAdd homAddEquiv	—	RingHomInvPair.ids
homMk_hom_apply 📖	mathematical	CategoryTheory.CategoryStruct.comp AddCommGrpCat CategoryTheory.Category.toCategoryStruct AddCommGrpCat.instCategory CategoryTheory.Functor.obj ModuleCat moduleCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup DFunLike.coe RingHom CategoryTheory.End CategoryTheory.Preadditive.instSemiringEnd AddCommGrpCat.instPreadditive RingHom.instFunLike smul	Hom.hom homMk CategoryTheory.ConcreteCategory.hom	—	—
hom_add 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instAddHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instAdd	—	—
hom_bijective 📖	mathematical	—	Function.Bijective Hom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule Hom.hom	—	—
hom_comp 📖	mathematical	—	Hom.hom CategoryTheory.CategoryStruct.comp ModuleCat CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap.comp carrier Ring.toSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids	—	—
hom_ext 📖	—	Hom.hom	—	—	Hom.ext
hom_ext_iff 📖	mathematical	—	Hom.hom	—	hom_ext
hom_id 📖	mathematical	—	Hom.hom CategoryTheory.CategoryStruct.id ModuleCat CategoryTheory.Category.toCategoryStruct moduleCategory LinearMap.id carrier Ring.toSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule	—	—
hom_injective 📖	mathematical	—	Hom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule Hom.hom	—	Function.Bijective.injective hom_bijective
hom_inv_apply 📖	mathematical	—	DFunLike.coe carrier CategoryTheory.ConcreteCategory.hom ModuleCat moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier CategoryTheory.Iso.hom CategoryTheory.Iso.inv	—	CategoryTheory.Iso.inv_hom_id_apply
hom_neg 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instNegHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instNeg	—	—
hom_nsmul 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instSMulNatHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule AddMonoid.toNatSMul SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup LinearMap.addCommGroup	—	—
hom_ofHom 📖	mathematical	—	Hom.hom of ofHom	—	—
hom_smul 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instSMulHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instSMul DistribMulAction.toDistribSMul AddCommMonoid.toAddMonoid	—	—
hom_sub 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instSubHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instSub	—	—
hom_sum 📖	mathematical	—	Hom.hom Finset.sum Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory AddCommGroup.toAddCommMonoid instAddCommGroupHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier isAddCommGroup isModule LinearMap.addCommMonoid	—	map_sum AddMonoidHom.instAddMonoidHomClass hom_zero hom_add
hom_surjective 📖	mathematical	—	Hom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule Hom.hom	—	Function.Bijective.surjective hom_bijective
hom_zero 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instZeroHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instZero	—	—
hom_zsmul 📖	mathematical	—	Hom.hom Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory instSMulIntHom LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule SubNegMonoid.toZSMul AddGroup.toSubNegMonoid AddCommGroup.toAddGroup LinearMap.addCommGroup	—	—
id_apply 📖	mathematical	—	DFunLike.coe carrier CategoryTheory.ConcreteCategory.hom ModuleCat moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier CategoryTheory.CategoryStruct.id CategoryTheory.Category.toCategoryStruct	—	—
instHasZeroObject 📖	mathematical	—	CategoryTheory.Limits.HasZeroObject ModuleCat moduleCategory	—	isZero_of_subsingleton
instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms ModuleCat moduleCategory AddCommGrpCat AddCommGrpCat.instCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup	—	CategoryTheory.Functor.map_isIso CategoryTheory.isIso_of_reflects_iso instReflectsIsomorphismsForgetLinearMapIdCarrier
instReflectsIsomorphismsForgetLinearMapIdCarrier 📖	mathematical	—	CategoryTheory.Functor.ReflectsIsomorphisms ModuleCat moduleCategory CategoryTheory.types CategoryTheory.forget LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier	—	RingHomInvPair.ids Equiv.left_inv Equiv.right_inv CategoryTheory.Iso.isIso_hom
inv_hom_apply 📖	mathematical	—	DFunLike.coe carrier CategoryTheory.ConcreteCategory.hom ModuleCat moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier CategoryTheory.Iso.inv CategoryTheory.Iso.hom	—	CategoryTheory.Iso.hom_inv_id_apply
isZero_iff_subsingleton 📖	mathematical	—	CategoryTheory.Limits.IsZero ModuleCat moduleCategory carrier	—	subsingleton_of_isZero isZero_of_subsingleton
isZero_of_iff_subsingleton 📖	mathematical	—	CategoryTheory.Limits.IsZero ModuleCat moduleCategory of	—	isZero_iff_subsingleton
isZero_of_subsingleton 📖	mathematical	—	CategoryTheory.Limits.IsZero ModuleCat moduleCategory	—	hom_ext LinearMap.ext map_zero AddMonoidHomClass.toZeroHomClass DistribMulActionSemiHomClass.toAddMonoidHomClass SemilinearMapClass.distribMulActionSemiHomClass LinearMap.semilinearMapClass
mkOfSMul'_smul 📖	mathematical	—	AddCommGrpCat.carrier mkOfSMul' instSMulCarrierMkOfSMul' DFunLike.coe CategoryTheory.ConcreteCategory.hom AddCommGrpCat AddCommGrpCat.instCategory AddMonoidHom AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier	—	—
mkOfSMul_smul 📖	mathematical	—	DFunLike.coe RingHom CategoryTheory.End AddCommGrpCat CategoryTheory.Category.toCategoryStruct AddCommGrpCat.instCategory CategoryTheory.Functor.obj ModuleCat moduleCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup mkOfSMul CategoryTheory.Preadditive.instSemiringEnd AddCommGrpCat.instPreadditive RingHom.instFunLike smul	—	—
ofHom_apply 📖	mathematical	—	DFunLike.coe of carrier CategoryTheory.ConcreteCategory.hom ModuleCat moduleCategory LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier ofHom	—	—
ofHom_comp 📖	mathematical	—	ofHom LinearMap.comp Ring.toSemiring AddCommGroup.toAddCommMonoid RingHom.id Semiring.toNonAssocSemiring RingHomCompTriple.ids CategoryTheory.CategoryStruct.comp ModuleCat CategoryTheory.Category.toCategoryStruct moduleCategory of	—	RingHomCompTriple.ids
ofHom_hom 📖	mathematical	—	ofHom carrier isAddCommGroup isModule Hom.hom	—	—
ofHom_id 📖	mathematical	—	ofHom LinearMap.id Ring.toSemiring AddCommGroup.toAddCommMonoid CategoryTheory.CategoryStruct.id ModuleCat CategoryTheory.Category.toCategoryStruct moduleCategory of	—	—
ofHom₂_hom_apply_hom 📖	mathematical	—	Hom.hom CommRing.toRing DFunLike.coe LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct moduleCategory AddCommGroup.toAddCommMonoid isAddCommGroup instAddCommGroupHom isModule Hom.instModule LinearMap.instFunLike of smulCommClass_self CommRing.toCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction ofHom₂ LinearMap.addCommMonoid LinearMap.module	—	smulCommClass_self
ofHom₂_hom₂ 📖	mathematical	—	ofHom₂ Hom.hom₂	—	smulCommClass_self
of_coe 📖	mathematical	—	of carrier isAddCommGroup isModule	—	—
smulNatTrans_apply_app 📖	mathematical	—	CategoryTheory.NatTrans.app ModuleCat moduleCategory AddCommGrpCat AddCommGrpCat.instCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup DFunLike.coe RingHom CategoryTheory.End CategoryTheory.Functor CategoryTheory.Category.toCategoryStruct CategoryTheory.Functor.category CategoryTheory.Preadditive.instSemiringEnd CategoryTheory.functorCategoryPreadditive AddCommGrpCat.instPreadditive RingHom.instFunLike smulNatTrans CategoryTheory.Functor.obj smul	—	—
smul_naturality 📖	mathematical	—	CategoryTheory.CategoryStruct.comp AddCommGrpCat CategoryTheory.Category.toCategoryStruct AddCommGrpCat.instCategory CategoryTheory.Functor.obj ModuleCat moduleCategory CategoryTheory.forget₂ LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup CategoryTheory.Functor.map DFunLike.coe RingHom CategoryTheory.End CategoryTheory.Preadditive.instSemiringEnd AddCommGrpCat.instPreadditive RingHom.instFunLike smul	—	AddCommGrpCat.hom_ext AddMonoidHom.ext LinearMap.map_smul
subsingleton_of_isZero 📖	mathematical	CategoryTheory.Limits.IsZero ModuleCat moduleCategory	carrier	—	LinearMap.id_apply hom_id CategoryTheory.Limits.IsZero.iff_id_eq_zero

ModuleCat.Algebra

Definitions

Name	Category	Theorems
instLinear 📖	CompOp	3 math math: MoritaEquivalence.linear, instLinearRestrictScalars, restrictScalarsEquivalenceOfRingEquiv_linear
instModuleCarrier 📖	CompOp	4 math math: instSMulCommClassCarrier, instIsScalarTowerCarrier, ModuleCat.monoidalClosed_pre_app, ModuleCat.ihom_ev_app

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
instIsScalarTowerCarrier 📖	mathematical	—	IsScalarTower ModuleCat.carrier Algebra.toSMul Ring.toSemiring SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup ModuleCat.isAddCommGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Module.toDistribMulAction AddCommGroup.toAddCommMonoid ModuleCat.isModule CommSemiring.toSemiring instModuleCarrier	—	Algebra.smul_def SemigroupAction.mul_smul
instSMulCommClassCarrier 📖	mathematical	—	SMulCommClass ModuleCat.carrier SMulZeroClass.toSMul AddZero.toZero AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup ModuleCat.isAddCommGroup DistribSMul.toSMulZeroClass DistribMulAction.toDistribSMul MonoidWithZero.toMonoid Semiring.toMonoidWithZero Ring.toSemiring Module.toDistribMulAction AddCommGroup.toAddCommMonoid ModuleCat.isModule CommSemiring.toSemiring instModuleCarrier	—	smul_assoc IsScalarTower.left smul_eq_mul Algebra.commutes SemigroupAction.mul_smul

ModuleCat.Hom

Definitions

Name	Category	Theorems
hom 📖	CompOp	230 math math: CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, Rep.resCoindHomEquiv_symm_apply_hom, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, Rep.resCoindHomEquiv_apply_hom, ModuleCat.hom_zero, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, Rep.MonoidalClosed.linearHomEquiv_symm_hom, groupCohomology.isoCocycles₁_hom_comp_i_apply, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, groupCohomology.d₂₃_hom_apply, LinearMap.id_fgModuleCat_comp, FGModuleCat.hom_hom_id, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, ModuleCat.toMatrixModCat_map, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, Rep.resCoindAdjunction_counit_app_hom_hom, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, ModuleCat.linearIndependent_shortExact, ModuleCat.monoidalClosed_uncurry, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, ModuleCat.Iso.homCongr_eq_arrowCongr, groupHomology.comap_coinvariantsKer_pOpcycles_range_subtype_pOpcycles_eq_top, groupCohomology.d₁₂_hom_apply, PresheafOfModules.pushforward_map_app_apply, PresheafOfModules.toSheafify_app_apply', LinearMap.comp_id_fgModuleCat, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, groupCohomology.d₀₁_hom_apply, ModuleCat.hom_surjective, ModuleCat.hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, Rep.resCoindAdjunction_unit_app_hom_hom, ModuleCat.endRingEquiv_symm_apply_hom, Rep.homEquiv_apply_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, Rep.coindFunctorIso_hom_app_hom_hom_apply_hom_hom_apply, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, PresheafOfModules.Derivation.postcomp_d_apply, Rep.indCoindIso_inv_hom_hom, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, Rep.ρ_hom, PresheafOfModules.pushforward_map_app_apply', groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, ModuleCat.MonoidalCategory.whiskerLeft_def, ModuleCat.hom_smul, Rep.MonoidalClosed.linearHomEquivComm_hom, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, FGModuleCat.hom_comp, ModuleCat.imageIsoRange_hom_subtype, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, ModuleCat.MonoidalCategory.tensorHom_def, ModuleCat.imageIsoRange_inv_image_ι_apply, Rep.indCoindIso_hom_hom_hom, PresheafOfModules.Monoidal.tensorObj_map_tmul, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, ModuleCat.monoidalClosed_curry, ModuleCat.homAddEquiv_symm_apply_hom, ModuleCat.range_eq_top_of_epi, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, ModuleCat.hom_whiskerRight, ModuleCat.hom_inv_associator, FGModuleCat.hom_id, ModuleCat.directLimitIsColimit_desc, Rep.indResAdjunction_counit_app_hom_hom, FDRep.hom_hom_action_ρ, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, ModuleCat.hom_whiskerLeft, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, ModuleCat.hom_hom_leftUnitor, ModuleCat.hom_hom_rightUnitor, ModuleCat.ker_eq_bot_of_mono, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, ModuleCat.imageIsoRange_hom_subtype_assoc, PresheafOfModules.pushforward_obj_map_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, Rep.coindFunctorIso_inv_app_hom_hom_apply_coe, groupCohomology.d₀₁_ker_eq_invariants, ModuleCat.hom_ext_iff, CoalgCat.ofComonObjCoalgebraStruct_comul, groupHomology.range_d₁₀_eq_coinvariantsKer, groupHomology.isoCycles₂_hom_comp_i_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierOfCarrierStalkAbPresheafPrimeComplAsIdealHomToStalk, ModuleCat.imageIsoRange_inv_image_ι, ModuleCat.hom_inv_rightUnitor, ModuleCat.hom_sum, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, groupHomology.π_comp_H1Iso_hom_apply, Rep.coindIso_inv_hom_hom, ModuleCat.hom_nsmul, groupCohomology.map_id_comp_H0Iso_hom_apply, groupHomology.chainsMap_id_f_hom_eq_mapRange, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, LinearMap.id_moduleCat_comp, Rep.diagonalSuccIsoTensorTrivial_hom_hom_single, Representation.linHom.invariantsEquivRepHom_symm_apply_coe, Rep.toCoinvariantsMkQ_hom, groupHomology.isoCycles₁_hom_comp_i_apply, FGModuleCat.Iso.conj_eq_conj, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, ModuleCat.imageIsoRange_inv_image_ι_assoc, groupCohomology.cochainsMap_f, inhomogeneousCochains.d_hom_apply, PresheafOfModules.DifferentialsConstruction.relativeDifferentials'_map_d, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_assoc, ModuleCat.kernelIsoKer_hom_ker_subtype, ModuleCat.hom_add, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, FGModuleCat.hom_hom_comp, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, FGModuleCat.hom_ext_iff, ModuleCat.hom_hom_associator, Rep.coinvariantsMk_app_hom, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, groupHomology.mapCycles₂_hom, groupHomology.isoCycles₂_inv_comp_iCycles_apply, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, Rep.ihom_map_hom, Rep.coinvariantsTensor_hom_ext_iff, ModuleCat.homMk_hom_apply, ModuleCat.hom_id, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, groupHomology.chainsMap_f_hom, Rep.indResAdjunction_unit_app_hom_hom, groupHomology.map_id_comp_H0Iso_hom_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom, ModuleCat.uliftFunctor_map, groupCohomology.mapCocycles₁_comp_i_apply, ModuleCat.hom_zsmul, ModuleCat.ofHom_hom, Rep.coindMap_hom, Rep.MonoidalClosed.linearHomEquiv_hom, Rep.invariantsAdjunction_homEquiv_apply_hom, ModuleCat.localizedModuleMap_hom_apply, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_hom_apply, groupCohomology.cochainsMap_f_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, MatrixModCat.toModuleCat_map, groupCohomology.π_comp_H2Iso_hom_apply, ModuleCat.HasLimit.lift_hom_apply, ModuleCat.binaryProductLimitCone_isLimit_lift, Rep.indMap_hom, Rep.homEquiv_symm_apply_hom, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, Rep.invariantsFunctor_map_hom, ModuleCat.Iso.conj_eq_conj, groupCohomology.π_comp_H1Iso_hom_apply, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, PresheafOfModules.pushforward_obj_map_apply', FGModuleCat.FGModuleCatEvaluation_apply', ModuleCat.hom_inv_leftUnitor, groupHomology.mapCycles₂_comp_i_apply, ModuleCat.ofHom₂_hom_apply_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, ModuleCat.hom_sub, CoalgCat.ofComonObjCoalgebraStruct_counit, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, Rep.leftRegularTensorTrivialIsoFree_hom_hom_single_tmul_single, ModuleCat.mono_iff_ker_eq_bot, groupHomology.π_comp_H1Iso_inv_apply, groupCohomology.isoCocycles₂_hom_comp_i_apply, ModuleCat.hom_bijective, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, ModuleCat.hom_ofHom, Rep.MonoidalClosed.linearHomEquivComm_symm_hom, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, Rep.indResHomEquiv_apply_hom, ModuleCat.homAddEquiv_apply, ModuleCat.span_rightExact, ModuleCat.endRingEquiv_apply, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, ModuleCat.hom_comp, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, ModuleCat.hom_neg, PresheafOfModules.toSheafify_app_apply, ModuleCat.MonoidalCategory.whiskerRight_def, ModuleCat.kernelIsoKer_inv_kernel_ι, ModuleCat.imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, FGModuleCat.Iso.conj_hom_eq_conj, ModuleCat.epi_iff_range_eq_top, ModuleCat.monoidalClosed_pre_app, Rep.coinvariantsFunctor_map_hom, ModuleCat.hom_injective, ModuleCat.CoextendScalars.map'_hom_apply_apply, Rep.coindIso_hom_hom_hom, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, FDRep.hom_action_ρ, ModuleCat.toKernelSubobject_arrow, CategoryTheory.Iso.toLinearMap_toLinearEquiv, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, groupHomology.π_comp_H2Iso_inv_apply, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, Rep.indResHomEquiv_symm_apply_hom, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, Rep.leftRegularTensorTrivialIsoFree_inv_hom_single_single, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.chainsMap_f, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, ModuleCat.forget₂_map
hom' 📖	CompOp	2 math math: ext_iff, hom₂_apply
hom₂ 📖	CompOp	3 math math: ModuleCat.ofHom₂_hom₂, hom₂_apply, hom₂_ofHom₂
instModule 📖	CompOp	9 math math: FGModuleCat.instFiniteHomModuleCatObjIsFG, ModuleCat.homLinearEquiv_symm_apply, FGModuleCat.ihom_obj, hom₂_apply, ModuleCat.homLinearEquiv_apply, ModuleCat.ofHom₂_hom_apply_hom, ModuleCat.ofHom₂_compr₂, ModuleCat.monoidalClosed_pre_app, ModuleCat.ihom_ev_app

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	hom'	—	—	—
ext_iff 📖	mathematical	—	hom'	—	ext
hom₂_apply 📖	mathematical	—	DFunLike.coe LinearMap CommSemiring.toSemiring CommRing.toCommSemiring RingHom.id Semiring.toNonAssocSemiring ModuleCat.carrier CommRing.toRing AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule LinearMap.addCommMonoid LinearMap.module smulCommClass_self CommRing.toCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction Ring.toSemiring LinearMap.instFunLike hom₂ Quiver.Hom ModuleCat CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct ModuleCat.moduleCategory ModuleCat.instAddCommGroupHom LinearMap.addCommGroup instModule hom' ModuleCat.of ModuleCat.ofHom LinearEquiv.toLinearMap ModuleCat.homLinearEquiv	—	smulCommClass_self
hom₂_ofHom₂ 📖	mathematical	—	hom₂ ModuleCat.ofHom₂	—	smulCommClass_self

ModuleCat.Hom.Simps

Definitions

Name	Category	Theorems
hom 📖	CompOp	—

ModuleCat.Iso

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
conj_eq_conj 📖	mathematical	—	DFunLike.coe MulEquiv CategoryTheory.End ModuleCat CommRing.toRing CategoryTheory.Category.toCategoryStruct ModuleCat.moduleCategory CategoryTheory.End.mul EquivLike.toFunLike MulEquiv.instEquivLike CategoryTheory.Iso.conj LinearEquiv CommSemiring.toSemiring CommRing.toCommSemiring RingHom.id Semiring.toNonAssocSemiring Ring.toSemiring RingHomInvPair.ids Module.End ModuleCat.carrier AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule LinearMap.addCommMonoid LinearMap.module smulCommClass_self CommSemiring.toCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction LinearEquiv.instEquivLike LinearEquiv.conj CategoryTheory.Iso.toLinearEquiv ModuleCat.Hom.hom	—	—
homCongr_eq_arrowCongr 📖	mathematical	—	DFunLike.coe Equiv Quiver.Hom ModuleCat CommRing.toRing CategoryTheory.CategoryStruct.toQuiver CategoryTheory.Category.toCategoryStruct ModuleCat.moduleCategory EquivLike.toFunLike Equiv.instEquivLike CategoryTheory.Iso.homCongr LinearEquiv CommSemiring.toSemiring CommRing.toCommSemiring RingHom.id Semiring.toNonAssocSemiring Ring.toSemiring RingHomInvPair.ids LinearMap ModuleCat.carrier AddCommGroup.toAddCommMonoid ModuleCat.isAddCommGroup ModuleCat.isModule LinearMap.addCommMonoid LinearMap.module smulCommClass_self CommSemiring.toCommMonoid DistribMulAction.toMulAction CommMonoid.toMonoid AddCommMonoid.toAddMonoid Module.toDistribMulAction LinearEquiv.instEquivLike LinearEquiv.arrowCongr RingHomCompTriple.ids CategoryTheory.Iso.toLinearEquiv ModuleCat.Hom.hom	—	—

(root)

Definitions

Name	Category	Theorems
linearEquivIsoModuleIso 📖	CompOp	2 math math: linearEquivIsoModuleIso_hom, linearEquivIsoModuleIso_inv

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
linearEquivIsoModuleIso_hom 📖	mathematical	—	CategoryTheory.Iso.hom CategoryTheory.types LinearEquiv Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids AddCommGroup.toAddCommMonoid CategoryTheory.Iso ModuleCat ModuleCat.moduleCategory ModuleCat.of linearEquivIsoModuleIso LinearEquiv.toModuleIso	—	RingHomInvPair.ids
linearEquivIsoModuleIso_inv 📖	mathematical	—	CategoryTheory.Iso.inv CategoryTheory.types LinearEquiv Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring RingHomInvPair.ids AddCommGroup.toAddCommMonoid CategoryTheory.Iso ModuleCat ModuleCat.moduleCategory ModuleCat.of linearEquivIsoModuleIso CategoryTheory.Iso.toLinearEquiv	—	RingHomInvPair.ids

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