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	807 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, 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, CategoryTheory.linearCoyoneda_obj_obj_carrier, groupCohomology.isoCocycles₁_hom_comp_i_apply, ContinuousCohomology.I_obj_V_isAddCommGroup, cokernel_π_ext, CategoryTheory.Iso.toCoalgEquiv_symm, forget_preservesLimitsOfSize, LightCondensed.ihomPoints_apply, LinearMap.id_fgModuleCat_comp, groupHomology.d₁₀_single_one, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, groupCohomology.δ_apply, FGModuleCat.hom_hom_id, 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, ContinuousCohomology.I_obj_V_carrier, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, groupHomology.d₃₂_single, TopModuleCat.hom_zero_apply, extendScalarsId_hom_app_one_tmul, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, FDRep.endRingEquiv_symm_comp_ρ, ι_coprodIsoDirectSum_hom_apply, restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, CoalgCat.of_comul, LightCondensed.ihomPoints_symm_comp, isZero_iff_subsingleton, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_carrier, AlternatingMap.postcomp_apply, QuadraticModuleCat.toIsometry_comp, linearIndependent_shortExact, Rep.invariantsFunctor_obj_carrier, monoidalClosed_uncurry, 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, directLimitCocone_pt_carrier, toMatrixModCat_obj_carrier, instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, PresheafOfModules.pushforward_map_app_apply, CategoryTheory.preadditiveYonedaObj_obj_carrier, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_carrier, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor, PresheafOfModules.sections_property, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_sub_apply, 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, toMatrixModCat_obj_isAddCommGroup, groupHomology.δ₀_apply, groupCohomology.cocycles₂.d₂₃_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, hom_surjective, TopModuleCat.coe_freeObj, Rep.preservesLimits_forget, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CoalgCat.tensorObj_isAddCommGroup, restrictScalars_η, 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, TopModuleCat.continuousSMul, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, endRingEquiv_symm_apply_hom, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, extendRestrictScalarsAdj_counit_app_apply_one_tmul, FilteredColimits.colimit_zero_eq, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, PresheafOfModules.pushforward₀_obj_obj_carrier, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_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, 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, PresheafOfModules.Derivation.d_one, PresheafOfModules.sectionsMap_coe, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, 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, Rep.ActionToRep_obj_ρ, isFG_iff, CategoryTheory.linearYoneda_obj_obj_carrier, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, homLinearEquiv_symm_apply, hom_smul, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, FGModuleCat.hom_comp, ContinuousCohomology.I_obj_ρ_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, imageIsoRange_hom_subtype, GradedObject.finrankSupport_subset_iff, CategoryTheory.Iso.toIsometryEquiv_toFun, CoextendScalars.smul_apply, binaryProductLimitCone_cone_π_app_right, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, HasColimit.colimitCocone_pt_isModule, Rep.ActionToRep_obj_V, PresheafOfModules.toPresheaf_obj_coe, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, Rep.instEpiModuleCatAppCoinvariantsMk, 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, TopModuleCat.coe_of, exteriorPower.map_mk, TopModuleCat.ofHom_hom, subsingleton_of_isZero, cokernel_π_cokernelIsoRangeQuotient_hom, Rep.ofModuleMonoidAlgebra_obj_coe, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, hom_inv_apply, 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, 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, ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, FilteredColimits.forget_preservesFilteredColimits, cokernel_π_imageSubobject_ext, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, forget₂_map_homMk, Rep.instFaithfulModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, groupCohomology.δ₁_apply, homAddEquiv_symm_apply_hom, groupHomology.coinvariantsMk_comp_H0Iso_inv, groupHomology.toCycles_comp_isoCycles₁_hom_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, CategoryTheory.ShortComplex.moduleCatMk_X₃_carrier, localizedModule_isLocalizedModule, range_eq_top_of_epi, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, Derivation.d_mul, 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, 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, Rep.RepToAction_map_hom, PresheafOfModules.Derivation.congr_d, MonoidalCategory.associator_def, 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, hom_whiskerLeft, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, 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, 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, Rep.coinvariantsFunctor_hom_ext_iff, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, CategoryTheory.whiskering_linearCoyoneda₂, FGModuleCat.obj_carrier, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.H1π_comp_map_apply, FGModuleCat.FGModuleCatCoevaluation_apply_one, span_exact, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MonoidalCategory.tensorLift_tmul, MatrixModCat.toModuleCat_obj_carrier, hom_hom_leftUnitor, PresheafOfModules.surjective_of_epi, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, adj_homEquiv, instIsScalarTowerLocalizationCarrierLocalizedModule, hom_hom_rightUnitor, biprodIsoProd_inv_comp_snd, CoalgCat.tensorUnit_carrier, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, CategoryTheory.Iso.toCoalgEquiv_refl, piIsoPi_inv_kernel_ι_apply, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, ker_eq_bot_of_mono, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_add_apply, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, MonModuleEquivalenceAlgebra.functor_obj_carrier, imageIsoRange_hom_subtype_assoc, QuadraticModuleCat.toIsometry_whiskerRight, PresheafOfModules.pushforward_obj_map_apply, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, LightCondensed.forget_map_hom_app, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, CoalgCat.forget_reflects_isos, groupCohomology.d₀₁_ker_eq_invariants, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, smulNatTrans_apply_app, FGModuleCat.ihom_obj, TopModuleCat.hom_id, forget_reflectsLimits, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, PresheafOfModules.forgetToPresheafModuleCatObjObj_coe, 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, LightCondensed.forget_obj_obj_map, SheafOfModules.pushforwardCongr_inv_app_val_app, QuadraticModuleCat.toIsometry_hom_rightUnitor, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, 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, Rep.ActionToRep_map, 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, PresheafOfModules.presheaf_obj_coe, hom_inv_rightUnitor, ExtendScalars.smul_tmul, PresheafOfModules.homMk_app, hom_sum, Rep.RepToAction_obj_V_carrier, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, extendsScalars_map_rightUnitor_inv_one_tmul, extendScalars_δ_tmul, CategoryTheory.Iso.toCoalgEquiv_trans, groupHomology.π_comp_H1Iso_hom_apply, hom_nsmul, groupCohomology.map_id_comp_H0Iso_hom_apply, forget_obj, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_nsmul_apply, PresheafOfModules.toPresheaf_map_app_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, PresheafOfModules.Derivation'.d_app, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, Rep.trivialFunctor_obj_V, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, coe_of, restrictScalars_μ_tmul, CategoryTheory.Iso.toIsometryEquiv_refl, QuadraticModuleCat.toIsometry_inv_rightUnitor, ExtendScalars.map_tmul, FilteredColimits.colimit_add_mk_eq', QuadraticModuleCat.cliffordAlgebra_map, Rep.preservesColimits_forget, FilteredColimits.forget_reflectsFilteredColimits, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, LinearMap.id_moduleCat_comp, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, QuadraticModuleCat.toIsometry_whiskerLeft, CategoryTheory.Iso.toLinearEquiv_apply, Derivation.d_map, SheafOfModules.pushforwardComp_hom_app_val_app, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, MonoidalCategory.tensorObj, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, 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, Profinite.NobelingProof.GoodProducts.square_commutes, groupHomology.d₃₂_single_one_fst, CoalgCat.MonoidalCategoryAux.counit_tensorObj, 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, 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, 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, PresheafOfModules.ofPresheaf_obj_carrier, hom_hom_associator, CoalgCat.forget₂_obj, Rep.coinvariantsAdjunction_unit_app, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, groupHomology.δ_apply, Rep.coinvariantsMk_app_hom, Rep.forget₂_moduleCat_obj, 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, QuadraticModuleCat.toIsometry_id, groupHomology.cyclesMk₂_eq, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, PresheafOfModules.Derivation.d_app, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zsmul_apply, 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, groupHomology.pOpcycles_comp_opcyclesIso_hom, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, TopModuleCat.hom_nsmul, Rep.RepToAction_obj_ρ, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, LightCondensed.ihomPoints_symm_apply, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, Derivation.d_add, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, groupHomology.H1AddEquivOfIsTrivial_apply, MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, homMk_hom_apply, TopModuleCat.instIsTopologicalAddGroupCarrier, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, linearIndependent_leftExact, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, groupCohomology.δ₀_apply, PresheafOfModules.Derivation'.app_apply, CoalgCat.forget₂_map, HasLimit.productLimitCone_cone_pt_carrier, piIsoPi_hom_ker_subtype, directLimitDiagram_obj_carrier, hom_id, groupCohomology.cocyclesMk₂_eq, disjoint_span_sum, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.forget₂_moduleCat_map, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, piIsoPi_inv_kernel_ι, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, 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, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, ofHom_hom, groupHomology.mapCycles₂_id_comp_apply, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, localizedModuleMap_hom_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, AlternatingMap.ext_iff, free_shortExact_finrank_add, CoalgCat.MonoidalCategoryAux.comul_tensorObj, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, projective_of_module_projective, MatrixModCat.toModuleCat_map, groupHomology.π_comp_H0Iso_hom, 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, ContinuousCohomology.I_obj_V_topologicalSpace, groupHomology.H0π_comp_H0Iso_hom, AlgCat.forget₂_module_map, FilteredColimits.M.mk_surjective, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Iso.conj_eq_conj, CoalgCat.toComon_map_hom, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, MonoidalCategory.tensorObj_def, Rep.invariantsAdjunction_counit_app, 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, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, 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, MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, groupCohomology.iCocycles_mk, 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, extendScalars_δ, 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, groupHomology.shortComplexH0_g, Rep.RepToAction_obj, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, CoalgCat.tensorObj_isModule, FreeMonoidal.εIso_hom_one, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, QuadraticModuleCat.toIsometry_inv_leftUnitor, 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, 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, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, CategoryTheory.ShortComplex.moduleCatMk_X₂_carrier, groupHomology.d₁₀_comp_coinvariantsMk_assoc, groupHomology.iCycles_mk, MonoidalCategory.whiskerLeft_apply, groupHomology.cyclesMk₀_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, CoalgCat.toCoalgHom_id, forget_map, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, TopModuleCat.hom_comp, smulShortComplex_X₃_isModule, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, span_rightExact, CommRingCat.KaehlerDifferential.ext_iff, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, PresheafOfModules.germ_ringCat_smul, groupCohomology.cocyclesMk₀_eq, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρOfIsNoetherianRing, endRingEquiv_apply, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, extendsScalars_map_leftUnitor_inv_one_tmul, CoalgCat.toCoalgHom_comp, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, Rep.coinvariantsAdjunction_homEquiv_apply_hom, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, 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, instInvertibleCarrierOutModuleCatValSkeleton, PresheafOfModules.toSheafify_app_apply, MonoidalCategory.whiskerRight_def, isScalarTower_of_algebra_moduleCat, Algebra.instIsScalarTowerCarrier, ofHom_apply, TannakaDuality.FiniteGroup.ofRightFDRep_hom, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, simple_iff_isSimpleModule', restrictScalarsCongr_inv_app, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, TopModuleCat.hom_neg, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, instFreeCarrierX₂ModuleCatProjectiveShortComplex, forget₂AddCommGroupIsEquivalence, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.d₂₁_single_ρ_add_single_inv_mul, HasLimit.productLimitCone_isLimit_lift, hom_injective, MonoidalCategory.tensorObj_carrier, CategoryTheory.preadditiveCoyoneda_obj, 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, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, extendScalars_μ, groupHomology.H0π_comp_H0Iso_hom_apply, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupCohomology.coe_mapCocycles₂, isSimpleModule_of_simple, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, 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, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, 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, groupHomology.π_comp_H2Iso_inv_apply, 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, FilteredColimits.colimit_add_mk_eq, free_hom_ext_iff, CategoryTheory.Iso.toIsometryEquiv_symm, groupHomology.H2π_eq_zero_iff, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.Iso.toIsometryEquiv_trans, MonoidalCategory.associator_inv_apply, QuadraticModuleCat.hom_hom_associator, groupHomology.δ₁_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, QuadraticModuleCat.hom_inv_associator, forget₂_map, toMatrixModCat_obj_isModule
endRingEquiv 📖	CompOp	10 math math: FDRep.endRingEquiv_symm_comp_ρ, endRingEquiv_symm_apply_hom, Rep.ActionToRep_obj_ρ, Rep.RepToAction_map_hom, Rep.ActionToRep_map, Rep.RepToAction_obj_ρ, FDRep.of_ρ, Rep.RepToAction_obj, endRingEquiv_apply, FDRep.endRingEquiv_comp_ρ
equivalenceSemimoduleCat 📖	CompOp	—
hasForgetToAddCommGroup 📖	CompOp	40 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, forget₂_map_homMk, 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, homMk_hom_apply, 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	441 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, instReflectsIsomorphismsForgetLinearMapIdCarrier, forget_preservesLimits, CommRingCat.KaehlerDifferential.map_d, MonoidalCategory.braiding_hom_apply, restrictScalars.map_apply, forget₂_reflectsLimitsOfSize, groupCohomology.isoCocycles₁_hom_comp_i_apply, cokernel_π_ext, forget_preservesLimitsOfSize, groupHomology.d₁₀_single_one, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, groupCohomology.δ_apply, freeHomEquiv_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, forget₂AddCommGroup_preservesLimitsOfSize, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, 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, monoidalClosed_uncurry, CondensedMod.isDiscrete_tfae, groupCohomology.coe_mapCocycles₁, PresheafOfModules.pushforward_map_app_apply, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor, PresheafOfModules.sections_property, CondensedMod.LocallyConstant.instFullModuleCatSheafCompHausCoherentTopologyConstantSheaf, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, QuadraticModuleCat.forget₂_map_associator_inv, groupHomology.δ₀_apply, groupCohomology.cocycles₂.d₂₃_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, Rep.preservesLimits_forget, groupHomology.isoCycles₁_inv_comp_iCycles_apply, restrictScalars_η, 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, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, extendRestrictScalarsAdj_counit_app_apply_one_tmul, 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, 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, groupCohomology.H1IsoOfIsTrivial_inv_apply, PresheafOfModules.map_comp_apply, biprodIsoProd_inv_comp_snd_apply, PresheafOfModules.pushforward_map_app_apply', groupCohomology.H2π_comp_map_apply, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, HasColimit.colimitCocone_pt_isModule, CategoryTheory.preadditiveYoneda_obj, Rep.standardComplex.εToSingle₀_comp_eq, Rep.instEpiModuleCatAppCoinvariantsMk, 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, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, 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, 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, ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, FilteredColimits.forget_preservesFilteredColimits, cokernel_π_imageSubobject_ext, groupCohomology.H2π_eq_iff, forget₂_map_homMk, Rep.instFaithfulModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, groupCohomology.δ₁_apply, groupHomology.coinvariantsMk_comp_H0Iso_inv, groupHomology.toCycles_comp_isoCycles₁_hom_apply, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, 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, Rep.coinvariantsFunctor_hom_ext_iff, 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, PresheafOfModules.surjective_of_epi, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, adj_homEquiv, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, piIsoPi_inv_kernel_ι_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, Derivation.desc_d, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, PresheafOfModules.pushforward_obj_map_apply, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, LightCondensed.forget_map_hom_app, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_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, LightCondensed.forget_obj_obj_map, 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, extendsScalars_map_rightUnitor_inv_one_tmul, extendScalars_δ_tmul, 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, restrictScalars_μ_tmul, ExtendScalars.map_tmul, Rep.preservesColimits_forget, 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, 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, CoalgCat.forget₂_obj, Rep.coinvariantsAdjunction_unit_app, groupHomology.δ_apply, Rep.coinvariantsMk_app_hom, Rep.forget₂_moduleCat_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, groupHomology.pOpcycles_comp_opcyclesIso_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, homMk_hom_apply, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, groupCohomology.δ₀_apply, CoalgCat.forget₂_map, groupCohomology.cocyclesMk₂_eq, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.forget₂_moduleCat_map, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, 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, 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.groupHomologyπOdd_eq_iff, groupHomology.π_comp_H0Iso_hom, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, groupHomology.H0π_comp_H0Iso_hom, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, 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, 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, groupCohomology.iCocycles_mk, 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, groupHomology.shortComplexH0_g, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, FreeMonoidal.εIso_hom_one, groupHomology.π_comp_H1Iso_inv_apply, FGModuleCat.instFullModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.isoCocycles₂_hom_comp_i_apply, extendRestrictScalarsAdj_unit_app_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, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, groupHomology.d₁₀_comp_coinvariantsMk_assoc, groupHomology.iCycles_mk, MonoidalCategory.whiskerLeft_apply, groupHomology.cyclesMk₀_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, forget_map, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, span_rightExact, CommRingCat.KaehlerDifferential.ext_iff, groupCohomology.cocyclesMk₀_eq, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρOfIsNoetherianRing, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, extendsScalars_map_leftUnitor_inv_one_tmul, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, Rep.coinvariantsAdjunction_homEquiv_apply_hom, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, MonoidalCategory.braiding_inv_apply, ofHom_apply, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, restrictScalarsCongr_inv_app, imageIsoRange_hom_subtype_apply, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, forget₂AddCommGroupIsEquivalence, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.d₂₁_single_ρ_add_single_inv_mul, 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, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupCohomology.coe_mapCocycles₂, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, toKernelSubobject_arrow, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, 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, 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.δ₁_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	14 math math: Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, FDRep.instFiniteDimensionalHom, FGModuleCat.instFiniteHom, Rep.instLinearModuleCatCoinvariantsFunctor, Rep.instLinearModuleCatInvariantsFunctor, FDRep.simple_iff_end_is_rank_one, instMonoidalLinear, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, finite_ext, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, ofHom₂_compr₂, instLinearUliftFunctor, FDRep.scalar_product_char_eq_finrank_equivariant, FDRep.finrank_hom_simple_simple
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	453 math math: groupHomology.mapShortComplexH2_τ₁, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, 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, 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, groupCohomology.toCocycles_comp_isoCocycles₂_hom_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃_apply, groupCohomology.cocyclesIso₀_hom_comp_f, groupCohomology.eq_d₀₁_comp_inv, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, 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, linearIndependent_shortExact, 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, endRingEquiv_symm_apply_hom, groupHomology.H1CoresCoinfOfTrivial_X₁, groupHomology.chainsMap_id_f_map_mono, groupCohomology.mapShortComplexH2_comp_assoc, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_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, groupCohomology.instMonoModuleCatFH1InfRes, smulShortComplex_X₃_isAddCommGroup, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.π_comp_H2Iso_inv_assoc, shortComplex_shortExact, biprodIsoProd_inv_comp_snd_apply, groupHomology.chainsMap_f_3_comp_chainsIso₃, groupHomology.eq_d₂₁_comp_inv, groupHomology.shortComplexH2_f, Rep.ActionToRep_obj_ρ, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, Module.Flat.lTensor_shortComplex_exact, Profinite.NobelingProof.succ_exact, groupCohomology.dArrowIso₀₁_hom_right, 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, FDRep.instFiniteDimensionalHom, groupCohomology.shortComplexH1_f, Rep.standardComplex.εToSingle₀_comp_eq, groupHomology.inhomogeneousChains.d_def, groupCohomology.comp_d₂₃_eq, cokernel_π_cokernelIsoRangeQuotient_hom, groupHomology.H1CoresCoinf_X₁, 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, groupHomology.toCycles_comp_isoCycles₁_hom_apply, 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, FGModuleCat.instFiniteHom, groupCohomology.cochainsMap_zero, smulShortComplex_X₁, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, groupHomology.map_chainsFunctor_shortExact, 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, Rep.RepToAction_map_hom, 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, kernelIsoKer_inv_kernel_ι_apply, groupHomology.isoShortComplexH1_hom, groupCohomology.isoCocycles₂_hom_comp_i, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, Rep.instLinearModuleCatCoinvariantsFunctor, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₂, span_exact, 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, groupHomology.chainsFunctor_obj, groupCohomology.instMonoModuleCatFShortComplexH0, biprodIsoProd_inv_comp_snd, Rep.instPreservesZeroMorphismsModuleCatInvariantsFunctor, groupHomology.d₁₀ArrowIso_inv_right, range_mkQ_cokernelIsoRangeQuotient_inv, groupCohomology.mapShortComplexH2_zero, groupHomology.chainsMap_id_f_map_epi, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupCohomology.mapShortComplex₂_exact, groupCohomology.cochainsMap_id_f_map_mono, groupHomology.chainsMap_id_comp, groupHomology.instEpiModuleCatGH1CoresCoinf, groupCohomology.mapShortComplexH1_id, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, groupHomology.mapShortComplexH1_id_comp, groupHomology.mapShortComplexH1_comp, 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, 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, Rep.ActionToRep_map, groupHomology.cyclesIso₀_inv_comp_iCycles, uliftFunctor_map_exact, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, groupCohomology.mapShortComplexH2_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, 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, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, 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, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, 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, groupCohomology.cocyclesMk₁_eq, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, groupCohomology.H1InfRes_X₁, groupHomology.shortComplexH0_exact, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, instAdditiveRestrictScalars, groupHomology.toCycles_comp_isoCycles₂_hom_apply, PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation, groupCohomology.mapCocycles₁_comp_i_assoc, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, instAdditiveUliftFunctor, free_shortExact, 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, 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, groupHomology.mapShortComplex₂_exact, kernelIsoKer_hom_ker_subtype_apply, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, 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, Rep.RepToAction_obj_ρ, groupCohomology.eq_d₂₃_comp_inv, instMonoidalLinear, groupCohomology.cochainsMap_f_map_mono, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_f, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, groupCohomology.isoShortComplexH1_hom, groupHomology.mapShortComplexH1_id, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, groupCohomology.isoCocycles₂_inv_comp_iCocycles, linearIndependent_leftExact, instAdditiveLocalizationLocalizedModuleFunctor, restrictScalarsEquivalenceOfRingEquiv_additive, inhomogeneousCochains.d_eq, groupHomology.H1CoresCoinfOfTrivial_exact, MoritaEquivalence.instAdditiveModuleCatFunctorEqv, groupHomology.chainsFunctor_map, groupCohomology.cocyclesMk₂_eq, groupHomology.instPreservesZeroMorphismsRepChainComplexModuleCatNatChainsFunctor, disjoint_span_sum, groupCohomology.cochainsMap_id_f_map_epi, groupHomology.chainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom, groupHomology.cyclesMk₁_eq, groupHomology.H1CoresCoinfOfTrivial_f, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, groupCohomology.H1InfRes_exact, groupCohomology.mapShortComplexH2_τ₂, groupCohomology.mapCocycles₁_comp_i_apply, ChainComplex.linearYonedaObj_d, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₁_isModule, groupCohomology.instAdditiveRepCochainComplexModuleCatNatCochainsFunctor, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, forget₂_addCommGrp_additive, Rep.FiniteCyclicGroup.homResolutionIso_hom_f_hom_apply, free_shortExact_finrank_add, groupCohomology.cochainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₁, groupHomology.H1CoresCoinfOfTrivial_g, 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, 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, shortComplex_exact, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, groupHomology.isoCycles₁_inv_comp_iCycles, groupHomology.chainsMap_zero, groupHomology.H1CoresCoinfOfTrivial_g_epi, free_shortExact_rank_add, 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, groupCohomology.map_cochainsFunctor_shortExact, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, localizedModuleFunctor_map_exact, ofHom₂_compr₂, hasKernels_moduleCat, groupHomology.shortComplexH0_g, Rep.RepToAction_obj, 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, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, groupHomology.inhomogeneousChains.d_eq, groupHomology.eq_d₂₁_comp_inv_apply, CategoryTheory.ShortComplex.moduleCatMk_X₂_carrier, groupCohomology.cochainsFunctor_map, groupHomology.iCycles_mk, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, groupCohomology.shortComplexH2_g, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, smulShortComplex_X₃_isModule, groupHomology.mapShortComplexH1_τ₃, span_rightExact, 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, FDRep.scalar_product_char_eq_finrank_equivariant, 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, groupCohomology.H1InfRes_f, Rep.instAdditiveModuleCatInvariantsFunctor, smulShortComplex_X₂, instFreeCarrierX₂ModuleCatProjectiveShortComplex, 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, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, 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, groupHomology.π_comp_H1Iso_inv_assoc, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, 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.instAdditiveModuleCatCoinvariantsFunctor, groupCohomology.cochainsFunctor_obj, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, Module.Flat.rTensor_shortComplex_exact, groupCohomology.mapCocycles₁_comp_i, FDRep.simple_iff_char_is_norm_one, 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, FDRep.finrank_hom_simple_simple, 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	23 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, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, 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	791 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, 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, groupCohomology.isoCocycles₁_hom_comp_i_apply, ContinuousCohomology.I_obj_V_isAddCommGroup, cokernel_π_ext, CategoryTheory.Iso.toCoalgEquiv_symm, forget_preservesLimitsOfSize, LinearMap.id_fgModuleCat_comp, groupHomology.d₁₀_single_one, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, groupCohomology.δ_apply, FGModuleCat.hom_hom_id, 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, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, groupHomology.d₃₂_single, TopModuleCat.hom_zero_apply, extendScalarsId_hom_app_one_tmul, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, 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, linearIndependent_shortExact, monoidalClosed_uncurry, 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, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, PresheafOfModules.pushforward_map_app_apply, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor, PresheafOfModules.sections_property, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_sub_apply, 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, toMatrixModCat_obj_isAddCommGroup, groupHomology.δ₀_apply, groupCohomology.cocycles₂.d₂₃_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, hom_surjective, Rep.preservesLimits_forget, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CoalgCat.tensorObj_isAddCommGroup, restrictScalars_η, 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, TopModuleCat.continuousSMul, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, endRingEquiv_symm_apply_hom, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, extendRestrictScalarsAdj_counit_app_apply_one_tmul, FilteredColimits.colimit_zero_eq, 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, CategoryTheory.Iso.toCoalgEquiv_toCoalgHom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_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, PresheafOfModules.Derivation.d_one, PresheafOfModules.sectionsMap_coe, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, 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, Rep.ActionToRep_obj_ρ, isFG_iff, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, homLinearEquiv_symm_apply, hom_smul, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, FGModuleCat.hom_comp, ContinuousCohomology.I_obj_ρ_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, imageIsoRange_hom_subtype, GradedObject.finrankSupport_subset_iff, CategoryTheory.Iso.toIsometryEquiv_toFun, CoextendScalars.smul_apply, 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.instEpiModuleCatAppCoinvariantsMk, 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, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, 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, 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, ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, FilteredColimits.forget_preservesFilteredColimits, cokernel_π_imageSubobject_ext, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, forget₂_map_homMk, Rep.instFaithfulModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, groupCohomology.δ₁_apply, homAddEquiv_symm_apply_hom, groupHomology.coinvariantsMk_comp_H0Iso_inv, PresheafOfModules.pushforward₀_obj_obj_isAddCommGroup, groupHomology.toCycles_comp_isoCycles₁_hom_apply, TannakaDuality.FiniteGroup.sumSMulInv_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, localizedModule_isLocalizedModule, range_eq_top_of_epi, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, Derivation.d_mul, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, instFiniteCarrier, 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, FDRep.average_char_eq_finrank_invariants, 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, Rep.RepToAction_map_hom, PresheafOfModules.Derivation.congr_d, MonoidalCategory.associator_def, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, forget₂_obj, FDRep.hom_hom_action_ρ, FGModuleCat.FGModuleCatDual_obj, groupHomology.pOpcycles_comp_opcyclesIso_hom_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, Rep.coinvariantsFunctor_hom_ext_iff, 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, span_exact, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MonoidalCategory.tensorLift_tmul, MatrixModCat.toModuleCat_obj_carrier, hom_hom_leftUnitor, PresheafOfModules.surjective_of_epi, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, adj_homEquiv, instIsScalarTowerLocalizationCarrierLocalizedModule, hom_hom_rightUnitor, biprodIsoProd_inv_comp_snd, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, CategoryTheory.Iso.toCoalgEquiv_refl, piIsoPi_inv_kernel_ι_apply, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, Rep.RepToAction_obj_V_isAddCommGroup, ker_eq_bot_of_mono, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_add_apply, CondensedMod.hom_naturality_apply, lof_coprodIsoDirectSum_inv_apply, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, imageIsoRange_hom_subtype_assoc, QuadraticModuleCat.toIsometry_whiskerRight, PresheafOfModules.pushforward_obj_map_apply, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, LightCondensed.forget_map_hom_app, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, CoalgCat.forget_reflects_isos, groupCohomology.d₀₁_ker_eq_invariants, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, smulNatTrans_apply_app, FGModuleCat.ihom_obj, TopModuleCat.hom_id, forget_reflectsLimits, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, FDRep.char_linHom, 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, LightCondensed.forget_obj_obj_map, SheafOfModules.pushforwardCongr_inv_app_val_app, QuadraticModuleCat.toIsometry_hom_rightUnitor, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, 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, Rep.ActionToRep_map, 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, PresheafOfModules.homMk_app, hom_sum, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, extendsScalars_map_rightUnitor_inv_one_tmul, extendScalars_δ_tmul, CategoryTheory.Iso.toCoalgEquiv_trans, groupHomology.π_comp_H1Iso_hom_apply, hom_nsmul, groupCohomology.map_id_comp_H0Iso_hom_apply, forget_obj, directLimitDiagram_obj_isAddCommGroup, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_nsmul_apply, PresheafOfModules.toPresheaf_map_app_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_exact_iff_function_exact, groupHomology.cyclesMap_comp_isoCycles₂_hom_apply, PresheafOfModules.Derivation'.d_app, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, restrictScalars_μ_tmul, CategoryTheory.Iso.toIsometryEquiv_refl, QuadraticModuleCat.toIsometry_inv_rightUnitor, ExtendScalars.map_tmul, FilteredColimits.colimit_add_mk_eq', QuadraticModuleCat.cliffordAlgebra_map, Rep.preservesColimits_forget, FilteredColimits.forget_reflectsFilteredColimits, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, LinearMap.id_moduleCat_comp, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, QuadraticModuleCat.toIsometry_whiskerLeft, CategoryTheory.Iso.toLinearEquiv_apply, Derivation.d_map, SheafOfModules.pushforwardComp_hom_app_val_app, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, MonoidalCategory.tensorObj, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, FGModuleCat.Iso.conj_eq_conj, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, 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, Profinite.NobelingProof.GoodProducts.square_commutes, groupHomology.d₃₂_single_one_fst, CoalgCat.MonoidalCategoryAux.counit_tensorObj, 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, FDRep.char_one, 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, TannakaDuality.FiniteGroup.sumSMulInv_single_id, TopModuleCat.isTopologicalAddGroup, groupCohomology.H1π_comp_map_apply, free_shortExact, hom_hom_associator, CoalgCat.forget₂_obj, Rep.coinvariantsAdjunction_unit_app, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, groupHomology.δ_apply, Rep.coinvariantsMk_app_hom, Rep.forget₂_moduleCat_obj, 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, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, PresheafOfModules.Derivation.d_app, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zsmul_apply, 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, groupHomology.pOpcycles_comp_opcyclesIso_hom, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, TopModuleCat.hom_nsmul, Rep.RepToAction_obj_ρ, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, Derivation.d_add, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, groupHomology.H1AddEquivOfIsTrivial_apply, MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, homMk_hom_apply, TopModuleCat.instIsTopologicalAddGroupCarrier, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, linearIndependent_leftExact, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, groupCohomology.δ₀_apply, PresheafOfModules.Derivation'.app_apply, CoalgCat.forget₂_map, piIsoPi_hom_ker_subtype, hom_id, groupCohomology.cocyclesMk₂_eq, disjoint_span_sum, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.forget₂_moduleCat_map, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, piIsoPi_inv_kernel_ι, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, 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, MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, ofHom_hom, groupHomology.mapCycles₂_id_comp_apply, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, localizedModuleMap_hom_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, free_shortExact_finrank_add, CoalgCat.MonoidalCategoryAux.comul_tensorObj, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, projective_of_module_projective, MatrixModCat.toModuleCat_map, groupHomology.π_comp_H0Iso_hom, 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, FGModuleCat.FGModuleCatDual_coe, groupHomology.H0π_comp_H0Iso_hom, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Iso.conj_eq_conj, CoalgCat.toComon_map_hom, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, MonoidalCategory.tensorObj_def, Rep.invariantsAdjunction_counit_app, FGModuleCat.instFiniteCarrier, 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.Iso.conj_ρ, FDRep.of_ρ, forget₂PreservesColimitsOfShape, MatrixModCat.toModuleCat_obj_isAddCommGroup, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, restrictScalars.smul_def', PresheafOfModules.pushforward_obj_map_apply', FDRep.char_dual, 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.iCocycles_mk, 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, extendScalars_δ, 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, groupHomology.shortComplexH0_g, Rep.RepToAction_obj, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, CoalgCat.tensorObj_isModule, FreeMonoidal.εIso_hom_one, QuadraticModuleCat.toIsometry_inv_leftUnitor, 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, 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, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, groupHomology.d₁₀_comp_coinvariantsMk_assoc, groupHomology.iCycles_mk, MonoidalCategory.whiskerLeft_apply, groupHomology.cyclesMk₀_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, CoalgCat.toCoalgHom_id, forget_map, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, TopModuleCat.hom_comp, smulShortComplex_X₃_isModule, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, span_rightExact, CommRingCat.KaehlerDifferential.ext_iff, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, PresheafOfModules.germ_ringCat_smul, groupCohomology.cocyclesMk₀_eq, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρOfIsNoetherianRing, endRingEquiv_apply, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, extendsScalars_map_leftUnitor_inv_one_tmul, CoalgCat.toCoalgHom_comp, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, Rep.coinvariantsAdjunction_homEquiv_apply_hom, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, 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, instInvertibleCarrierOutModuleCatValSkeleton, PresheafOfModules.toSheafify_app_apply, MonoidalCategory.whiskerRight_def, isScalarTower_of_algebra_moduleCat, Algebra.instIsScalarTowerCarrier, ofHom_apply, TannakaDuality.FiniteGroup.ofRightFDRep_hom, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, simple_iff_isSimpleModule', restrictScalarsCongr_inv_app, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, TopModuleCat.hom_neg, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, FGModuleCat.Iso.conj_hom_eq_conj, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, forget₂AddCommGroupIsEquivalence, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.d₂₁_single_ρ_add_single_inv_mul, HasLimit.productLimitCone_isLimit_lift, hom_injective, MonoidalCategory.tensorObj_carrier, CategoryTheory.preadditiveCoyoneda_obj, 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, extendScalars_μ, groupHomology.H0π_comp_H0Iso_hom_apply, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, FDRep.hom_action_ρ, MonoidalCategory.tensorUnit_isAddCommGroup, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupCohomology.coe_mapCocycles₂, isSimpleModule_of_simple, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, 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, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, 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, groupHomology.π_comp_H2Iso_inv_apply, 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, 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, QuadraticModuleCat.hom_hom_associator, groupHomology.δ₁_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, QuadraticModuleCat.hom_inv_associator, forget₂_map, toMatrixModCat_obj_isModule
isModule 📖	CompOp	766 math math: HasColimit.colimitCocone_pt_isAddCommGroup, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, TopModuleCat.hom_cokerπ, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, hom_zero, 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, restrictScalars.map_apply, forget₂_reflectsLimitsOfSize, groupCohomology.isoCocycles₁_hom_comp_i_apply, PresheafOfModules.ofPresheaf_obj_isModule, cokernel_π_ext, CategoryTheory.Iso.toCoalgEquiv_symm, forget_preservesLimitsOfSize, LinearMap.id_fgModuleCat_comp, groupHomology.d₁₀_single_one, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, TopModuleCat.instPreservesLimitTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrierOfHasLimitOfModuleCatCompLinearMapForget, groupCohomology.δ_apply, FGModuleCat.hom_hom_id, 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, CoalgCat.MonoidalCategoryAux.tensorHom_toLinearMap, groupHomology.d₃₂_single, TopModuleCat.hom_zero_apply, extendScalarsId_hom_app_one_tmul, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, 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, QuadraticModuleCat.toIsometry_comp, linearIndependent_shortExact, monoidalClosed_uncurry, 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, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, PresheafOfModules.pushforward_map_app_apply, CategoryTheory.ShortComplex.moduleCatMk_X₂_isModule, FGModuleCat.instPreservesFiniteColimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor, 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, groupHomology.δ₀_apply, groupCohomology.cocycles₂.d₂₃_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.d₃₂_single_one_thd, hom_surjective, Rep.preservesLimits_forget, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, CoalgCat.tensorObj_isAddCommGroup, restrictScalars_η, 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, TopModuleCat.continuousSMul, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, forget₂AddCommGroup_reflectsLimitOfShape, forget_reflectsLimitsOfSize, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, endRingEquiv_symm_apply_hom, CoalgCat.MonoidalCategoryAux.counit_tensorObj_tensorObj_right, FGModuleCat.instFiniteHomModuleCatObjIsFG, extendRestrictScalarsAdj_counit_app_apply_one_tmul, 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, CategoryTheory.Iso.toCoalgEquiv_toCoalgHom, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_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, PresheafOfModules.sectionsMap_coe, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, 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', Rep.ActionToRep_obj_ρ, isFG_iff, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, homLinearEquiv_symm_apply, hom_smul, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, FGModuleCat.hom_comp, ContinuousCohomology.I_obj_ρ_apply, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, imageIsoRange_hom_subtype, GradedObject.finrankSupport_subset_iff, CategoryTheory.Iso.toIsometryEquiv_toFun, CoextendScalars.smul_apply, 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.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, Rep.instEpiModuleCatAppCoinvariantsMk, 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, TopModuleCat.ofHom_hom, cokernel_π_cokernelIsoRangeQuotient_hom, id_apply, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, FGModuleCat.instPreservesFiniteLimitsModuleCatForget₂LinearMapIdCarrierObjIsFG, groupCohomology.d₁₂_apply_mem_cocycles₂, Rep.invariantsAdjunction_unit_app, hom_inv_apply, 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, 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, ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, FilteredColimits.forget_preservesFilteredColimits, cokernel_π_imageSubobject_ext, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, forget₂_map_homMk, Rep.instFaithfulModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, groupCohomology.δ₁_apply, homAddEquiv_symm_apply_hom, groupHomology.coinvariantsMk_comp_H0Iso_inv, groupHomology.toCycles_comp_isoCycles₁_hom_apply, TannakaDuality.FiniteGroup.sumSMulInv_apply, Module.Flat.iff_lTensor_preserves_shortComplex_exact, localizedModule_isLocalizedModule, range_eq_top_of_epi, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, PresheafOfModules.mono_iff_surjective, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, Derivation.d_mul, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, instFiniteCarrier, 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, FDRep.average_char_eq_finrank_invariants, 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, CategoryTheory.preadditiveYonedaObj_obj_isModule, groupHomology.mapCycles₁_id_comp_apply, MonoidalCategory.rightUnitor_def, CategoryTheory.Iso.toLinearEquiv_symm, PresheafOfModules.presheaf_map_apply_coe, smulShortComplex_g, Rep.RepToAction_map_hom, MonoidalCategory.associator_def, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, mono_iff_injective, forget₂_obj, FDRep.hom_hom_action_ρ, FGModuleCat.FGModuleCatDual_obj, groupHomology.pOpcycles_comp_opcyclesIso_hom_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, Rep.coinvariantsFunctor_hom_ext_iff, 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, span_exact, groupHomology.π_comp_H0Iso_hom_apply, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, groupCohomology.eq_d₀₁_comp_inv_apply, MonoidalCategory.tensorLift_tmul, MatrixModCat.toModuleCat_obj_carrier, hom_hom_leftUnitor, PresheafOfModules.surjective_of_epi, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, adj_homEquiv, instIsScalarTowerLocalizationCarrierLocalizedModule, hom_hom_rightUnitor, 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, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, QuadraticModuleCat.forget₂_map_associator_hom, PresheafOfModules.injective_of_mono, free_ε_one, imageIsoRange_hom_subtype_assoc, QuadraticModuleCat.toIsometry_whiskerRight, PresheafOfModules.pushforward_obj_map_apply, groupHomology.d₁₀_comp_coinvariantsMk, groupHomology.d₂₁_comp_d₁₀_apply, LightCondensed.forget_map_hom_app, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, CoalgCat.forget_reflects_isos, groupCohomology.d₀₁_ker_eq_invariants, CoalgCat.MonoidalCategoryAux.leftUnitor_hom_toLinearMap, smulNatTrans_apply_app, FGModuleCat.ihom_obj, TopModuleCat.hom_id, forget_reflectsLimits, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, FDRep.char_linHom, 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, LightCondensed.forget_obj_obj_map, SheafOfModules.pushforwardCongr_inv_app_val_app, QuadraticModuleCat.toIsometry_hom_rightUnitor, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, 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, Rep.ActionToRep_map, 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, PresheafOfModules.homMk_app, hom_sum, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, Rep.RepToAction_obj_V_isModule, extendsScalars_map_rightUnitor_inv_one_tmul, extendScalars_δ_tmul, CategoryTheory.Iso.toCoalgEquiv_trans, groupHomology.π_comp_H1Iso_hom_apply, hom_nsmul, 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, restrictScalars_μ_tmul, CategoryTheory.Iso.toIsometryEquiv_refl, QuadraticModuleCat.toIsometry_inv_rightUnitor, ExtendScalars.map_tmul, QuadraticModuleCat.cliffordAlgebra_map, Rep.preservesColimits_forget, FilteredColimits.forget_reflectsFilteredColimits, LinearMap.id_moduleCat_comp, free_μ_freeMk_tmul_freeMk, forget₂_obj_moduleCat_of, QuadraticModuleCat.toIsometry_whiskerLeft, CategoryTheory.Iso.toLinearEquiv_apply, SheafOfModules.pushforwardComp_hom_app_val_app, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, MonoidalCategory.tensorObj, groupHomology.isoCycles₁_hom_comp_i_apply, SheafOfModules.Presentation.map_relations_I, FGModuleCat.Iso.conj_eq_conj, instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, 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, Profinite.NobelingProof.GoodProducts.square_commutes, groupHomology.d₃₂_single_one_fst, CoalgCat.MonoidalCategoryAux.counit_tensorObj, 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, FDRep.char_one, 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, TannakaDuality.FiniteGroup.sumSMulInv_single_id, groupCohomology.H1π_comp_map_apply, free_shortExact, hom_hom_associator, CoalgCat.forget₂_obj, Rep.coinvariantsAdjunction_unit_app, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, groupHomology.δ_apply, Rep.coinvariantsMk_app_hom, Rep.forget₂_moduleCat_obj, 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, QuadraticModuleCat.toIsometry_id, groupHomology.cyclesMk₂_eq, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, 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, groupHomology.pOpcycles_comp_opcyclesIso_hom, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, TopModuleCat.hom_nsmul, Rep.RepToAction_obj_ρ, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, MonoidalCategory.whiskerRight_apply, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, homMk_hom_apply, free_δ_freeMk, forget₂AddCommGroup_reflectsLimitOfSize, linearIndependent_leftExact, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, CoalgCat.MonoidalCategoryAux.comul_tensorObj_tensorObj_right, groupCohomology.δ₀_apply, CoalgCat.forget₂_map, piIsoPi_hom_ker_subtype, hom_id, groupCohomology.cocyclesMk₂_eq, disjoint_span_sum, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, Rep.forget₂_moduleCat_map, AlgCat.forget₂Module_preservesLimits, groupHomology.d₃₂_apply_mem_cycles₂, MonoidalCategory.tensorUnit_isModule, piIsoPi_inv_kernel_ι, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, 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, groupCohomology.mapCocycles₁_comp_i_apply, hom_zsmul, ofHom_hom, groupHomology.mapCycles₂_id_comp_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_isModule, FGModuleCat.instLinearModuleCatForget₂LinearMapIdCarrierObjIsFG, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, localizedModuleMap_hom_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, free_shortExact_finrank_add, CoalgCat.MonoidalCategoryAux.comul_tensorObj, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, projective_of_module_projective, MatrixModCat.toModuleCat_map, groupHomology.π_comp_H0Iso_hom, 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, FGModuleCat.FGModuleCatDual_coe, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.linearYoneda_obj_obj_isModule, AlgCat.forget₂_module_map, FDRep.forget₂_ρ, extendScalarsComp_hom_app_one_tmul, Iso.conj_eq_conj, CoalgCat.toComon_map_hom, groupCohomology.π_comp_H1Iso_hom_apply, Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eq, MonoidalCategory.tensorObj_def, Rep.invariantsAdjunction_counit_app, FGModuleCat.instFiniteCarrier, 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_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.Iso.conj_ρ, FDRep.of_ρ, forget₂PreservesColimitsOfShape, MatrixModCat.toModuleCat_obj_isAddCommGroup, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, biproductIsoPi_inv_comp_π_apply, groupHomology.mapCycles₁_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, restrictScalars.smul_def', PresheafOfModules.pushforward_obj_map_apply', FDRep.char_dual, free_shortExact_rank_add, FGModuleCat.FGModuleCatEvaluation_apply', forget₂AddCommGroup_reflectsLimit, groupHomology.coe_mapCycles₁, 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.iCocycles_mk, 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, extendScalars_δ, 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, groupHomology.shortComplexH0_g, Rep.RepToAction_obj, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, CoalgCat.tensorObj_isModule, FreeMonoidal.εIso_hom_one, QuadraticModuleCat.toIsometry_inv_leftUnitor, 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, 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, SheafOfModules.pushforwardNatTrans_app_val_app_apply, CategoryTheory.whiskering_linearYoneda₂, groupHomology.d₁₀_comp_coinvariantsMk_assoc, groupHomology.iCycles_mk, MonoidalCategory.whiskerLeft_apply, groupHomology.cyclesMk₀_eq, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, CoalgCat.toCoalgHom_id, CoalgCat.tensorUnit_isModule, forget_map, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, TopModuleCat.hom_comp, smulShortComplex_X₃_isModule, homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, directLimitCocone_pt_isModule, span_rightExact, CommRingCat.KaehlerDifferential.ext_iff, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, PresheafOfModules.germ_ringCat_smul, groupCohomology.cocyclesMk₀_eq, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρOfIsNoetherianRing, endRingEquiv_apply, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, extendsScalars_map_leftUnitor_inv_one_tmul, CoalgCat.toCoalgHom_comp, mono_as_hom'_subtype, extendScalarsId_inv_app_apply, semilinearMapAddEquiv_symm_apply_apply, Rep.coinvariantsAdjunction_homEquiv_apply_hom, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, hom_comp, MonoidalCategory.braiding_inv_apply, 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, instInvertibleCarrierOutModuleCatValSkeleton, PresheafOfModules.toSheafify_app_apply, MonoidalCategory.whiskerRight_def, isScalarTower_of_algebra_moduleCat, Algebra.instIsScalarTowerCarrier, 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, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, TopModuleCat.hom_neg, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, FGModuleCat.Iso.conj_hom_eq_conj, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, forget₂AddCommGroupIsEquivalence, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, groupHomology.d₂₁_single_ρ_add_single_inv_mul, HasLimit.productLimitCone_isLimit_lift, hom_injective, MonoidalCategory.tensorObj_carrier, CategoryTheory.preadditiveCoyoneda_obj, 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, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, extendScalars_μ, groupHomology.H0π_comp_H0Iso_hom_apply, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, FDRep.hom_action_ρ, CategoryTheory.linearCoyoneda_obj_obj_isModule, FDRep.dualTensorIsoLinHom_hom_hom, ExtendScalars.hom_ext_iff, groupCohomology.coe_mapCocycles₂, isSimpleModule_of_simple, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, toKernelSubobject_arrow, CategoryTheory.Iso.toLinearMap_toLinearEquiv, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, 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, groupHomology.π_comp_H2Iso_inv_apply, 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, FilteredColimits.colimit_add_mk_eq, free_hom_ext_iff, CategoryTheory.Iso.toIsometryEquiv_symm, groupHomology.H2π_eq_zero_iff, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, CategoryTheory.Iso.toIsometryEquiv_trans, MonoidalCategory.associator_inv_apply, QuadraticModuleCat.hom_hom_associator, groupHomology.δ₁_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, QuadraticModuleCat.hom_inv_associator, forget₂_map, 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	1471 math math: HasColimit.colimitCocone_pt_isAddCommGroup, instIsRightAdjointCoextendScalars, instPreservesMonomorphismsRestrictScalars, PresheafOfModules.Monoidal.tensorObj_obj, groupHomology.mapShortComplexH2_τ₁, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, 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, 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, projective_of_free, groupCohomology.isoCocycles₁_hom_comp_i_apply, instEssentiallySmallFGModuleCat, groupHomology.map₁_quotientGroupMk'_epi, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, MoritaEquivalence.linear, groupHomology.coinfNatTrans_app, cokernel_π_ext, groupHomology.mapShortComplexH2_id, forget_preservesLimitsOfSize, restrictScalarsCongr_symm, LightCondensed.ihomPoints_apply, CategoryTheory.projectiveDimension_eq_of_semiLinearEquiv, LinearMap.id_fgModuleCat_comp, restrictScalarsId'App_inv_naturality_assoc, groupHomology.d₁₀_single_one, groupHomology.shortComplexH1_f, FDRep.char_tensor, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, forget₂PreservesColimitsOfSize, groupCohomology.inhomogeneousCochains.d_def, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, groupCohomology.δ_apply, PresheafOfModules.add_app, FGModuleCat.hom_hom_id, CondensedMod.IsSolid.isIso_solidification_map, groupCohomology.cocyclesMap_id_comp_assoc, groupHomology.map₁_one, groupHomology.mono_δ_of_isZero, groupCohomology.d₀₁_comp_d₁₂, 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, groupCohomology.cocyclesIso₀_hom_comp_f, groupHomology.d₃₂_single, CategoryTheory.Abelian.FreydMitchell.instFaithfulModuleCatEmbeddingRingFunctor, groupCohomology.eq_d₀₁_comp_inv, extendScalarsId_hom_app_one_tmul, groupCohomology.H1π_comp_map_assoc, injectiveDimension_eq_iSup_localizedModule_prime, groupHomology.mapCycles₁_comp_apply, groupHomology.cyclesIso₀_inv_comp_iCycles_apply, 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, isZero_iff_subsingleton, groupHomology.mapShortComplexH2_zero, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.whiskering_linearCoyoneda, cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_carrier, 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, localizedModuleFunctor_map, groupHomology.chainsMap_id, linearIndependent_shortExact, instSmallUnitsSkeletonModuleCat, Rep.invariantsFunctor_obj_carrier, monoidalClosed_uncurry, groupCohomology.H0IsoOfIsTrivial_hom, matrixEquivalence_inverse, TannakaDuality.FiniteGroup.forget_obj, CondensedMod.isDiscrete_tfae, CategoryTheory.linearYoneda_obj_map, SheafOfModules.evaluationPreservesLimit, hasLimits', CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, SheafOfModules.forgetToSheafModuleCat_map_hom, 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, preservesFiniteLimits_extendScalars_of_flat, instSmallSubtypeForallCarrierObjMemSubmoduleSectionsSubmodule, instAB4StarModuleCat, groupHomology.comp_d₂₁_eq, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, PresheafOfModules.pushforward_map_app_apply, PresheafOfModules.limitPresheafOfModules_map, CategoryTheory.preadditiveYonedaObj_obj_carrier, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_carrier, 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, CategoryTheory.Limits.Concrete.colimit_no_zero_smul_divisor, Rep.instIsTrivialObjModuleCatTrivialFunctor, PresheafOfModules.sections_property, groupHomology.H0π_comp_map, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_sub_apply, linearEquivIsoModuleIso_hom, groupHomology.H1CoresCoinf_X₃, groupCohomology.mapShortComplex₃_exact, 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, hasInjectiveDimensionLE_iff_forall_maximalSpectrum, 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, AlgebraicGeometry.tilde.map_sub, groupCohomology.comp_d₁₂_eq, toMatrixModCat_obj_isAddCommGroup, groupHomology.δ₀_apply, groupCohomology.cocycles₂.d₂₃_apply, extendRestrictScalarsAdj_homEquiv_apply, groupHomology.π_comp_H1Iso_inv, groupHomology.d₃₂_single_one_thd, CategoryTheory.ShortComplex.moduleCatMk_g, LightCondMod.isDiscrete_tfae, Rep.preservesLimits_forget, restrictScalarsComp'_inv_app, hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, groupHomology.coresNatTrans_app, restrictScalars_η, PresheafOfModules.free_map_app, Rep.instIsEquivalenceModuleCatMonoidAlgebraOfModuleMonoidAlgebra, 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, CategoryTheory.Abelian.freyd_mitchell, PresheafOfModules.freeYonedaEquiv_symm_app, 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, LinearEquiv.toModuleIso_inv, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, SheafOfModules.evaluationPreservesLimitsOfShape, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, forget₂AddCommGroup_reflectsLimitOfShape, exteriorPower.iso₀_hom_naturality, forget_reflectsLimitsOfSize, instIsEquivalenceFGModuleCatUlift, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, restrictScalars_isEquivalence_of_ringEquiv, groupHomology.d₃₂_comp_d₂₁_assoc, CoalgCat.comonEquivalence_inverse, endRingEquiv_symm_apply_hom, FGModuleCat.instFiniteHomModuleCatObjIsFG, restrictScalarsComp'_hom_app, groupHomology.H1CoresCoinfOfTrivial_X₁, extendRestrictScalarsAdj_counit_app_apply_one_tmul, groupHomology.chainsMap_id_f_map_mono, FilteredColimits.colimit_zero_eq, groupCohomology.mapShortComplexH2_comp_assoc, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, instPreservesFiniteLimitsLocalizationLocalizedModuleFunctor, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, instHasFiniteColimits, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, localizedModuleFunctor_obj, PresheafOfModules.id_app, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.full, MonoidalCategory.associator_hom_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, AlgebraicGeometry.instAdditiveModuleCatCarrierModulesSpecOfFunctor, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, HasLimit.productLimitCone_cone_π, HasColimit.colimitCocone_ι_app, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, PresheafOfModules.restrictScalarsObj_obj, instHasSeparatorModuleCatOfSmall, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, postcomp_extClass_surjective_of_projective_X₂, groupCohomology.instMonoModuleCatFH1InfRes, smulShortComplex_X₃_isAddCommGroup, forget₂_addCommGroup_full, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, hasLimitsOfSize, PresheafOfModules.sectionsMap_coe, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.d₁₀_comp_coinvariantsMk_apply, ExtendRestrictScalarsAdj.Counit.map_hom_apply, groupCohomology.H1IsoOfIsTrivial_inv_apply, groupHomology.π_comp_H2Iso_inv_assoc, shortComplex_shortExact, 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, Rep.instIsEquivalenceModuleCatMonoidAlgebraToModuleMonoidAlgebra, Rep.ActionToRep_obj_ρ, groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, CategoryTheory.linearYoneda_obj_obj_carrier, Rep.instLinearModuleCatObjFunctorCoinvariantsTensor, MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, groupHomology.mapCycles₁_comp, Module.Flat.lTensor_shortComplex_exact, groupHomology.map_comp, homLinearEquiv_symm_apply, Profinite.NobelingProof.succ_exact, hom_smul, groupCohomology.dArrowIso₀₁_hom_right, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, uliftFunctorForgetIso_hom_app, groupCohomology.π_map_assoc, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, smul_naturality, CategoryTheory.ShortComplex.moduleCat_zero_apply, groupCohomology.toCocycles_comp_isoCocycles₂_hom, Rep.instIsRightAdjointModuleCatInvariantsFunctor, groupCohomology.map_comp, FGModuleCat.hom_comp, SheafOfModules.evaluationPreservesLimitsOfSize, groupHomology.map_id_comp, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_assoc, CategoryTheory.faithful_linearYoneda, FDRep.instFullRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, imageIsoRange_hom_subtype, AlgebraicGeometry.isIso_fromTildeΓ_of_presentation, groupHomology.mapCycles₁_comp_i, CoextendScalars.smul_apply, Rep.coinvariantsTensorIndIso_inv, groupCohomology.shortComplexH0_f, binaryProductLimitCone_cone_π_app_right, groupCohomology.shortComplexH0_g, exteriorPower.desc_mk, PresheafOfModules.unit_map_one, groupHomology.functor_obj, PresheafOfModules.zsmul_app, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, FDRep.instFiniteDimensionalHom, matrixEquivalence_functor, HasColimit.colimitCocone_pt_isModule, Rep.ActionToRep_obj_V, groupCohomology.shortComplexH1_f, hasLimits, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.linearCoyoneda_obj_obj_isAddCommGroup, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, MonoidalCategory.tensorHom_def, groupHomology.inhomogeneousChains.d_def, PresheafOfModules.isoMk_hom_app, Rep.instEpiModuleCatAppCoinvariantsMk, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapId, restrictScalarsId'App_inv_naturality, 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, restrictScalarsId'_inv_app, AlgebraicGeometry.instFullModuleCatCarrierModulesSpecOfFunctor, PresheafOfModules.Monoidal.tensorObj_map_tmul, exteriorPower.map_mk, cokernel_π_cokernelIsoRangeQuotient_hom, extendScalars_assoc_assoc, groupHomology.H1CoresCoinf_X₁, Rep.ofModuleMonoidAlgebra_obj_coe, 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, 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, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, Rep.coinvariantsFunctor_obj_carrier, 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, ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.projectiveDimension_eq_of_linearEquiv, FilteredColimits.forget_preservesFilteredColimits, cokernel_π_imageSubobject_ext, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.cochainsMap_f_map_epi, groupCohomology.comp_d₀₁_eq, forget₂_map_homMk, FGModuleCat.instIsMonoidalClosedModuleCatIsFG, instPreservesInjectiveObjectsLocalizationLocalizedModuleFunctorOfIsNoetherianRing, Rep.instFaithfulModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, restrictScalarsId'App_hom_naturality_assoc, groupCohomology.δ₁_apply, homAddEquiv_symm_apply_hom, LinearMap.shortExact_shortComplexKer, 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, ExtendScalars.map'_id, PresheafOfModules.freeObj_map, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, FGModuleCat.instFiniteHom, groupCohomology.cochainsMap_zero, smulShortComplex_X₁, groupCohomology.dArrowIso₀₁_inv_left, groupCohomology.π_comp_H1Iso_hom, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, groupHomology.map_comp_assoc, instFiniteCarrier, Rep.coinvariantsTensorIndNatIso_inv_app, groupHomology.mapShortComplex₃_exact, groupHomology.epi_δ_of_isZero, PresheafOfModules.limitCone_π_app_app, AlgebraicGeometry.tilde.isoTop_hom, groupHomology.map_chainsFunctor_shortExact, 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, hom_inv_associator, PresheafOfModules.instEpiModuleCatCarrierObjOppositeRingCatApp, FGModuleCat.hom_id, groupCohomology.H1InfRes_X₂, lof_coprodIsoDirectSum_inv, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, groupCohomology.map₁_one, localizedModule_hasProjectiveDimensionLE, 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.epi_δ_of_isZero, groupCohomology.cochainsMap_id_comp, PresheafOfModules.presheaf_map_apply_coe, smulShortComplex_g, directLimitCocone_pt_isAddCommGroup, precomp_extClass_surjective_of_projective_X₂, 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, Rep.RepToAction_map_hom, restrictScalarsComp'App_hom_naturality_assoc, 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, FDRep.hom_hom_action_ρ, instPreservesFiniteColimitsLocalizationLocalizedModuleFunctor, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesInjectiveObjects, FGModuleCat.FGModuleCatDual_obj, AlgebraicGeometry.tilde.functor_map, groupHomology.pOpcycles_comp_opcyclesIso_hom_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, instPreservesProjectiveObjectsLocalizationLocalizedModuleFunctor, 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, 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, groupHomology.coe_mapCycles₂, Rep.coinvariantsFunctor_hom_ext_iff, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, LightCondensed.instPreservesEpimorphismsFunctorDiscreteNatLightCondModLim, CategoryTheory.whiskering_linearCoyoneda₂, FGModuleCat.obj_carrier, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, groupHomology.comp_d₁₀_eq, groupHomology.H1π_comp_map_apply, Rep.instLinearModuleCatCoinvariantsFunctor, LightCondensed.free_lightProfinite_internallyProjective_iff_tensor_condition', FGModuleCat.FGModuleCatCoevaluation_apply_one, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₂, groupHomology.H0π_comp_map_assoc, instHasExtModuleCatOfSmall, span_exact, 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, MatrixModCat.toModuleCat_obj_carrier, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, hom_hom_leftUnitor, groupHomology.chainsFunctor_obj, groupCohomology.mapCocycles₁_one, 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, hom_hom_rightUnitor, biprodIsoProd_inv_comp_snd, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, piIsoPi_inv_kernel_ι_apply, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, MonModuleEquivalenceAlgebra.functor_map_hom_apply, Rep.RepToAction_obj_V_isAddCommGroup, Rep.instPreservesZeroMorphismsModuleCatInvariantsFunctor, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_add_apply, CondensedMod.hom_naturality_apply, instIsLeftAdjointRestrictScalars, lof_coprodIsoDirectSum_inv_apply, Condensed.instIsRightKanExtensionFintypeCatCondensedModProfiniteProfiniteSolidProfiniteSolidCounit, groupHomology.d₁₀ArrowIso_inv_right, Derivation.desc_d, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, 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.π_comp_H0Iso_hom_assoc, groupCohomology.π_map, CategoryTheory.full_linearCoyoneda, TannakaDuality.FiniteGroup.forget_map, MonModuleEquivalenceAlgebra.functor_obj_carrier, imageIsoRange_hom_subtype_assoc, groupCohomology.mapShortComplexH2_zero, CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyonedaObj, PresheafOfModules.pushforward_obj_map_apply, groupHomology.chainsMap_id_f_map_epi, groupCohomology.H2π_comp_map_assoc, groupHomology.d₁₀_comp_coinvariantsMk, CategoryTheory.hasProjectiveDimensionLE_of_semiLinearEquiv, groupHomology.d₂₁_comp_d₁₀_apply, hasInjectiveDimensionLE_iff_forall_primeSpectrum, AlgebraicGeometry.tilde.isIso_toOpen_top, LightCondensed.forget_map_hom_app, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, groupHomology.mapCycles₂_comp_apply, groupCohomology.mapShortComplex₂_exact, CategoryTheory.faithful_linearCoyoneda, smulNatTrans_apply_app, FGModuleCat.ihom_obj, groupCohomology.cochainsMap_id_f_map_mono, CoalgCat.comonEquivalence_functor, groupHomology.chainsMap_id_comp, forget_reflectsLimits, TannakaDuality.FiniteGroup.equivApp_hom, uliftFunctorForgetIso_inv_app, FDRep.char_linHom, groupHomology.instEpiModuleCatGH1CoresCoinf, groupCohomology.mapShortComplexH1_id, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, reflectsIsomorphisms_extendScalars_of_faithfullyFlat, ExtendRestrictScalarsAdj.homEquiv_symm_apply, groupHomology.H1AddEquivOfIsTrivial_single, LightCondMod.instReflectsEpimorphismsLightCondSetForget, CategoryTheory.preservesFiniteColimits_preadditiveCoyonedaObj_of_projective, groupHomology.mapShortComplexH1_id_comp, CoalgCat.ofComonObjCoalgebraStruct_comul, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, groupHomology.mapShortComplexH1_comp, PresheafOfModules.unitHomEquiv_apply_coe, 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, LightCondensed.forget_obj_obj_map, SheafOfModules.pushforwardCongr_inv_app_val_app, groupCohomology.toCocycles_comp_isoCocycles₁_hom_assoc, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, 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, 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.mapShortComplexH2_τ₁, Rep.ActionToRep_map, FGModuleRepr.instIsEquivalenceFGModuleCatEmbed, groupHomology.cyclesIso₀_inv_comp_iCycles, instReflectsIsomorphismsRestrictScalars, exteriorPower.iso₁_hom_apply, FGModuleCat.instHasFiniteColimits, groupCohomology.d₁₂_comp_d₂₃_assoc, uliftFunctor_map_exact, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, PresheafOfModules.evaluation_preservesLimit, 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, Rep.RepToAction_obj_V_carrier, restrictScalarsComp'App_hom_naturality, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, Rep.RepToAction_obj_V_isModule, extendsScalars_map_rightUnitor_inv_one_tmul, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, extendScalars_δ_tmul, groupCohomology.mapShortComplexH2_id_comp_assoc, groupHomology.mapCycles₂_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, hom_nsmul, groupHomology.mapShortComplexH2_comp, groupCohomology.map_id_comp_H0Iso_hom_apply, forget_obj, directLimitDiagram_obj_isAddCommGroup, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_nsmul_apply, 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, FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, instIsRightAdjointForgetLinearMapIdCarrier, homEquiv_extendScalarsComp, restrictScalars_μ_tmul, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, QuadraticModuleCat.toModuleCat_tensor, ExtendScalars.map_tmul, FilteredColimits.colimit_add_mk_eq', PresheafOfModules.map_comp, Rep.preservesColimits_forget, FilteredColimits.forget_reflectsFilteredColimits, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, RingCat.moduleCatRestrictScalarsPseudofunctor_map, 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, FDRep.instHasKernels, instHasZeroObject, PresheafOfModules.evaluation_preservesColimitsOfSize, groupHomology.isoShortComplexH1_inv, SheafOfModules.pushforwardComp_hom_app_val_app, groupHomology.eq_d₁₀_comp_inv_assoc, groupCohomology.d₁₂_comp_d₂₃, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, 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, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, imageIsoRange_inv_image_ι_assoc, MonoidalCategory.rightUnitor_inv_apply, groupCohomology.H1π_eq_zero_iff, PresheafOfModules.sub_app, groupHomology.cyclesMap_comp_cyclesIso₀_hom, PresheafOfModules.colimitPresheafOfModules_map, Profinite.NobelingProof.GoodProducts.square_commutes, groupCohomology.cochainsMap_f, groupHomology.d₃₂_single_one_fst, 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.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, 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, FDRep.instInjectiveOfNeZeroCastCard, MonoidalCategory.tensorμ_apply, Rep.isZero_Tor_succ_of_projective, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, groupCohomology.H1InfRes_X₁, FDRep.char_one, groupHomology.shortComplexH0_exact, MonoidalCategory.tensorObj_isModule, Rep.instEpiModuleCatToModuleCatHom, groupHomology.inhomogeneousChains.ext_iff, FGModuleCat.hom_ext_iff, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, CategoryTheory.Abelian.FreydMitchell.instPreservesFiniteLimitsModuleCatEmbeddingRingFunctor, MonoidalCategory.tensorObj_isAddCommGroup, groupHomology.d₂₁_apply_mem_cycles₁, 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.H2π_eq_zero_iff, Rep.coinvariantsTensorIndNatIso_hom_app, groupHomology.π_map_assoc, PresheafOfModules.instAdditiveModuleCatCarrierObjOppositeRingCatEvaluation, groupCohomology.mapCocycles₁_comp_i_assoc, Rep.standardComplex.quasiIso_forget₂_εToSingle₀, instAdditiveUliftFunctor, TannakaDuality.FiniteGroup.sumSMulInv_single_id, PresheafOfModules.Hom.naturality_assoc, groupCohomology.H1π_comp_map_apply, free_shortExact, groupHomology.eq_d₃₂_comp_inv_assoc, projectiveDimension_le_projectiveDimension_of_isLocalizedModule, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, hom_hom_associator, CoalgCat.forget₂_obj, Rep.coinvariantsAdjunction_unit_app, groupCohomology.π_comp_H2Iso_hom_assoc, groupCohomology.H1InfRes_g, instHasLimitsOfSizeLightCondMod_1, CategoryTheory.preservesHomology_preadditiveYonedaObj_of_injective, CategoryTheory.linearCoyoneda_obj_map, groupCohomology.toCocycles_comp_isoCocycles₂_hom_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isModule_smul_apply, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₃, FDRep.simple_iff_end_is_rank_one, groupHomology.δ_apply, matrixEquivalence_counitIso, Rep.coinvariantsMk_app_hom, CategoryTheory.linearYoneda_obj_additive, Rep.instIsEquivalenceActionModuleCatRepToAction, groupHomology.shortComplexH2_g, Rep.forget₂_moduleCat_obj, 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.isoCycles₂_inv_comp_iCycles_apply, range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, mkOfSMul_smul, groupCohomology.instPreservesZeroMorphismsRepModuleCatFunctor, groupHomology.isoShortComplexH2_hom, LightCondMod.LocallyConstant.instFaithfulModuleCatFunctor, instMonoι, groupHomology.mapShortComplex₂_exact, 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, groupCohomology.mapShortComplexH1_comp, CategoryTheory.Limits.Concrete.colimit_rep_eq_zero, groupCohomology.mapShortComplex₁_exact, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_assoc, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zsmul_apply, 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, hasProjectiveDimensionLE_iff_forall_primeSpectrum, 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, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, groupHomology.π_comp_H2Iso_inv, Rep.RepToAction_obj_ρ, 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, groupHomology.instEpiModuleCatH1π, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, piIsoPi_hom_ker_subtype_apply, reflectsColimitsOfShape, FGModuleCat.instHasLimitsOfShapeOfFinCategory, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, MonoidalCategory.whiskerRight_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, homMk_hom_apply, instPreservesLimitsOfSizeUliftFunctor, free_δ_freeMk, FGModuleCat.instFullUlift, forget₂AddCommGroup_reflectsLimitOfSize, PresheafOfModules.instMonoModuleCatCarrierObjOppositeRingCatApp, linearIndependent_leftExact, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, instAdditiveLocalizationLocalizedModuleFunctor, FilteredColimits.ι_colimitDesc, groupCohomology.δ₀_apply, hasProjectiveDimensionLE_iff_forall_maximalSpectrum, CoalgCat.forget₂_map, Rep.unit_iso_comm, restrictScalarsEquivalenceOfRingEquiv_additive, inhomogeneousCochains.d_eq, HasLimit.productLimitCone_cone_pt_carrier, groupHomology.instEpiModuleCatH2π, groupHomology.H1CoresCoinfOfTrivial_exact, MoritaEquivalence.instAdditiveModuleCatFunctorEqv, piIsoPi_hom_ker_subtype, directLimitDiagram_obj_carrier, groupHomology.chainsFunctor_map, groupHomology.mapShortComplex₁_exact, hom_id, groupCohomology.cocyclesMk₂_eq, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, extendScalars_id_comp_assoc, injectiveDimension_le_injectiveDimension_of_isLocalizedModule, groupHomology.instPreservesZeroMorphismsRepChainComplexModuleCatNatChainsFunctor, disjoint_span_sum, LinearEquiv.toFGModuleCatIso_hom, TopModuleCat.instIsRightAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, AlgebraicGeometry.instFaithfulModuleCatCarrierModulesSpecOfFunctor, groupCohomology.cochainsMap_id_f_map_epi, instAB5ModuleCat, groupHomology.H1π_comp_map, groupHomology.chainsMap_f_hom, Rep.forget₂_moduleCat_map, 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, ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, extendScalars_η, projectiveDimension_eq_iSup_localizedModule_maximal, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, Rep.instLinearModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.map_id_comp_H0Iso_hom_apply, extendScalars_id_comp, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom, AlgebraicGeometry.tilde.map_add, RingCat.moduleCatRestrictScalarsPseudofunctor_mapComp, groupHomology.cyclesMk₁_eq, groupHomology.H1CoresCoinfOfTrivial_f, LightCondMod.epi_iff_locallySurjective_on_lightProfinite, PresheafOfModules.instHasLimitModuleCatCarrierObjOppositeRingCatCompEvaluationRestrictScalarsHomMap, groupHomology.cyclesIso₀_comp_H0π_assoc, 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, 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, instHasFiniteLimitsLightCondMod, groupHomology.mapCycles₂_id_comp_apply, ChainComplex.linearYonedaObj_d, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, finite_ext, 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, 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, SheafOfModules.pushforwardNatTrans_app_val_app, groupHomology.H2π_comp_map_apply, Hom.hom₂_apply, 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, LightCondensed.epi_π_app_zero_of_epi, groupCohomology.H1Map_id, free_shortExact_finrank_add, groupCohomology.cochainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatMkOfKerLERange_X₁, groupHomology.H1CoresCoinfOfTrivial_g, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, PresheafOfModules.instHasColimitModuleCatCarrierObjOppositeRingCatCompEvaluationRestrictScalarsHomMap, 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, FGModuleCat.FGModuleCatDual_coe, instHasLimitsOfSizeLightCondMod, instProjectiveObjFree, groupHomology.H0π_comp_H0Iso_hom, CategoryTheory.Abelian.FreydMitchell.instPreservesFiniteColimitsModuleCatEmbeddingRingFunctor, groupHomology.isoCycles₁_hom_comp_i_assoc, 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, FDRep.char_orthonormal, 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, MonoidalCategory.tensorObj_def, AlgebraicGeometry.tilde.map_zero, preservesFiniteLimits_tensorLeft_of_ringHomFlat, Rep.invariantsAdjunction_counit_app, FGModuleCat.instFiniteCarrier, groupHomology.d₂₁_single_one_snd, SheafOfModules.pushforwardPushforwardEquivalence_unit_app_val_app, groupCohomology.mapShortComplexH2_id_comp, groupHomology.π_comp_H0IsoOfIsTrivial_hom_assoc, CategoryTheory.ShortComplex.moduleCatMk_X₃_isModule, biprodIsoProd_inv_comp_fst, groupHomology.π_map_apply, CategoryTheory.Abelian.FreydMitchell.instFullModuleCatEmbeddingRingFunctor, instIsLeftAdjointExtendScalars, groupHomology.d₃₂_comp_d₂₁, groupHomology.d₃₂_single_one_snd, groupHomology.instEpiModuleCatGShortComplexH0, CategoryTheory.IsGrothendieckAbelian.instIsLeftAdjointModuleCatMulOppositeEndTensorObj, extendScalars_comp_id_assoc, 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, SheafOfModules.forgetToSheafModuleCat_obj_obj, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, biproductIsoPi_inv_comp_π_apply, shortComplex_exact, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, 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, free_shortExact_rank_add, groupHomology.cyclesMap_comp_isoCycles₁_hom_assoc, groupHomology.isIso_δ_of_isZero, 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, groupCohomology.d₀₁_comp_d₁₂_apply, Module.Flat.instPreservesFiniteLimitsModuleCatTensorLeftOfCarrier, free_map_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, 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, groupCohomology.subtype_comp_d₀₁, MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, groupCohomology.iCocycles_mk, 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, groupCohomology.map_cochainsFunctor_shortExact, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, groupHomology.d₁₀_single_inv, groupHomology.mkH1OfIsTrivial_apply, extendScalars_δ, groupCohomology.π_map_apply, LightCondensed.instCountableAB4StarLightCondMod, hom_sub, localCohomology.hasColimitDiagram, CoalgCat.ofComonObjCoalgebraStruct_counit, Rep.instMonoModuleCatToModuleCatHom, groupCohomology.cocyclesMap_id_comp, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.preservesFiniteLimits, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, CategoryTheory.Presieve.FamilyOfElements.isCompatible_map_smul_aux, localizedModuleFunctor_map_exact, instHasLimitsOfSize, ofHom₂_compr₂, CategoryTheory.hasProjectiveDimensionLE_of_linearEquiv, LightCondMod.LocallyConstant.instFullModuleCatLightCondensedDiscrete, extendScalars_comp_id, PresheafOfModules.freeYonedaEquiv_comp, forget₂AddCommGroup_preservesLimit, hasKernels_moduleCat, groupHomology.shortComplexH0_g, Rep.RepToAction_obj, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, FreeMonoidal.εIso_hom_one, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, groupCohomology.mapShortComplexH2_id, groupHomology.d₁₀ArrowIso_hom_right, groupCohomology.shortComplexH0_exact, 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, AlgebraicGeometry.tilde.map_comp, groupHomology.d₂₁_single, Rep.instIsEquivalenceActionModuleCatActionToRep, 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, SheafOfModules.pushforwardNatTrans_app_val_app_apply, extendScalars_ε, PresheafOfModules.colimitCocone_ι_app_app, CategoryTheory.whiskering_linearYoneda₂, CategoryTheory.ShortComplex.moduleCatMk_X₂_carrier, groupCohomology.cochainsFunctor_map, groupHomology.d₁₀_comp_coinvariantsMk_assoc, PresheafOfModules.colimitPresheafOfModules_obj, groupHomology.iCycles_mk, MonoidalCategory.whiskerLeft_apply, PresheafOfModules.Finite.evaluation_preservesFiniteColimits, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, groupCohomology.shortComplexH2_g, forget_map, instIsGrothendieckAbelianModuleCat, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapId, CategoryTheory.preadditiveCoyonedaObj_obj_isModule, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, FDRep.instProjectiveOfNeZeroCastCard, PresheafOfModules.limitPresheafOfModules_obj, groupHomology.H0π_comp_H0Iso_hom_assoc, groupCohomology.H1π_comp_map, groupHomology.cyclesMap_comp, LightCondensed.internallyProjective_iff_tensor_condition', smulShortComplex_X₃_isModule, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, 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, span_rightExact, instLinearUliftFunctor, CommRingCat.KaehlerDifferential.ext_iff, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, groupCohomology.cocyclesMk₀_eq, AlgebraicGeometry.tilde.map_neg, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρOfIsNoetherianRing, endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, directLimitDiagram_map, ofHom_id, LightCondensed.instIsGrothendieckAbelianLightCondMod, HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, groupCohomology.isoShortComplexH1_inv, image.fac, CategoryTheory.additive_coyonedaObj, extendsScalars_map_leftUnitor_inv_one_tmul, 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, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, hom_neg, FDRep.scalar_product_char_eq_finrank_equivariant, instInvertibleCarrierOutModuleCatValSkeleton, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, MonoidalCategory.whiskerRight_def, AlgebraicGeometry.isIso_fromTildeΓ_iff, FGModuleCat.instFaithfulUlift, groupCohomology.cochainsMap_id_comp_assoc, preservesLimit_restrictScalars, 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, LightCondensed.instEpiLightCondModMapNat, kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, AlgebraicGeometry.tilde.map_id_assoc, simple_iff_isSimpleModule', groupHomology.shortComplexH1_g, Rep.instPreservesZeroMorphismsModuleCatCoinvariantsFunctor, restrictScalarsCongr_inv_app, groupCohomology.eq_d₁₂_comp_inv_assoc, groupHomology.cyclesMap_id, projectiveDimension_eq_iSup_localizedModule_prime, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.preservesFiniteColimits_embedding, groupCohomology.H1InfRes_f, Rep.instAdditiveModuleCatInvariantsFunctor, imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, FGModuleCat.Iso.conj_hom_eq_conj, smulShortComplex_X₂, MatrixModCat.toModuleCat_obj_isModule, epi_iff_range_eq_top, instFreeCarrierX₂ModuleCatProjectiveShortComplex, forget₂AddCommGroupIsEquivalence, groupHomology.d₁₀ArrowIso_inv_left, monoidalClosed_pre_app, groupHomology.H1AddEquivOfIsTrivial_symm_tmul, Rep.coinvariantsFunctor_map_hom, 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, injectiveDimension_eq_iSup_localizedModule_maximal, MonoidalCategory.tensorObj_carrier, 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, groupHomology.eq_d₁₀_comp_inv_apply, LinearEquiv.toFGModuleCatIso_inv, semilinearMapAddEquiv_apply, CoextendScalars.map'_hom_apply_apply, TannakaDuality.FiniteGroup.equivHom_surjective, RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, freeHomEquiv_symm_apply, ulift_injective_of_injective, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, TannakaDuality.FiniteGroup.equivHom_injective, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, extendScalars_μ, groupHomology.H0π_comp_H0Iso_hom_apply, freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, groupHomology.mapShortComplexH2_τ₃, FDRep.hom_action_ρ, MonoidalCategory.tensorUnit_isAddCommGroup, PresheafOfModules.evaluation_map, CategoryTheory.linearCoyoneda_obj_obj_isModule, FDRep.dualTensorIsoLinHom_hom_hom, homEquiv_extendScalarsId, ExtendScalars.hom_ext_iff, 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, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom_assoc, Condensed.instAB4CondensedMod, groupCohomology.H1π_eq_iff, groupHomology.chainsMap_f_1_comp_chainsIso₁_apply, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, smulShortComplex_g_epi, Rep.Tor_obj, groupCohomology.mono_δ_of_isZero, groupCohomology.isoCocycles₁_hom_comp_i_assoc, groupHomology.π_comp_H1Iso_inv_assoc, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, CategoryTheory.ShortComplex.ShortExact.moduleCat_injective_f, 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, smulShortComplex_exact, groupHomology.π_comp_H2Iso_inv_apply, PresheafOfModules.evaluation_preservesColimit, CoalgCat.toComon_obj, Rep.instAdditiveModuleCatCoinvariantsFunctor, PresheafOfModules.forgetToPresheafModuleCat_map, MonModuleEquivalenceAlgebra.inverseObj_one, localizedModule_hasInjectiveDimensionLE, groupCohomology.cochainsFunctor_obj, restrictScalarsComp'App_inv_apply, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, isZero_of_subsingleton, isZero_of_iff_subsingleton, Module.Flat.rTensor_shortComplex_exact, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, groupCohomology.mapCocycles₁_comp_i, 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, 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, groupCohomology.isIso_δ_of_isZero, MonoidalCategory.associator_inv_apply, preservesColimit_restrictScalars, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, isSeparator, instHasFiniteBiproducts, exteriorPower.functor_map, groupHomology.δ₁_apply, instEnoughInjectivesModuleCatInt, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.H1π_eq_iff, ExtendRestrictScalarsAdj.unit_app, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, FDRep.finrank_hom_simple_simple, FGModuleCat.instIsIsoCoimageImageComparison, CoextendScalars.map_apply, groupCohomology.shortComplexH1_g, groupHomology.chainsMap_f, 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, ChainComplex.linearYonedaObj_X, toMatrixModCat_obj_isModule
of 📖	CompOp	466 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, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom_assoc, 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, 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, groupHomology.H0IsoOfIsTrivial_inv_eq_π, 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, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_apply, groupHomology.mapCycles₁_comp_assoc, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_assoc, groupHomology.toCycles_comp_isoCycles₂_hom_assoc, groupHomology.H0π_comp_map, linearEquivIsoModuleIso_hom, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂, RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, groupCohomology.comp_d₁₂_eq, groupHomology.δ₀_apply, 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, LinearEquiv.toModuleIso_inv, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, exteriorPower.iso₀_hom_naturality, ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, groupHomology.d₃₂_comp_d₂₁_assoc, endRingEquiv_symm_apply_hom, extendRestrictScalarsAdj_counit_app_apply_one_tmul, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_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, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_assoc, groupCohomology.d₁₂_apply_mem_cocycles₂, groupHomology.mapCycles₂_id_comp, groupCohomology.d₀₁_apply_mem_cocycles₁, exteriorPower.iso₀_hom_apply, groupHomology.cyclesMap_comp_cyclesIso₀_hom_apply, groupHomology.d₂₁_single_inv_self_ρ_sub_self_inv, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, groupCohomology.subtype_comp_d₀₁_apply, ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.comp_d₀₁_eq, groupCohomology.δ₁_apply, 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, groupHomology.cyclesIso₀_comp_H0π_apply, 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, Rep.RepToAction_map_hom, groupCohomology.instEpiModuleCatH1π, IsProjective.iff_projective, groupCohomology.H2π_comp_map, groupHomology.π_comp_H2Iso_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, groupHomology.cyclesIso₀_inv_comp_cyclesMap_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, groupHomology.H0π_comp_map_assoc, groupCohomology.dArrowIso₀₁_hom_left, groupCohomology.cocyclesMap_comp_isoCocycles₁_hom, groupHomology.toCycles_comp_isoCycles₁_hom_assoc, groupHomology.π_comp_H0Iso_hom_apply, 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, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, 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, 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, groupHomology.π_comp_H0IsoOfIsTrivial_hom, 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, groupHomology.cyclesIso₀_inv_comp_iCycles, groupCohomology.d₁₂_comp_d₂₃_assoc, ExtendScalars.smul_tmul, QuadraticModuleCat.forget₂_obj, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, extendsScalars_map_rightUnitor_inv_one_tmul, 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, 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, groupHomology.cyclesMap_comp_cyclesIso₀_hom, 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, groupHomology.chainsMap_f_0_comp_chainsIso₀_assoc, Rep.instEpiModuleCatToModuleCatHom, 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, Rep.forget₂_moduleCat_obj, 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.pOpcycles_comp_opcyclesIso_hom, groupHomology.H2π_comp_map, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Module.injective_iff_injective_object, groupHomology.cyclesIso₀_inv_comp_cyclesMap_assoc, Rep.RepToAction_obj_ρ, groupCohomology.eq_d₂₃_comp_inv, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv, groupHomology.H1π_comp_map_assoc, groupHomology.instEpiModuleCatH1π, piIsoPi_hom_ker_subtype_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, groupCohomology.δ₀_apply, 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, groupHomology.pOpcycles_comp_opcyclesIso_hom_assoc, groupCohomology.toCocycles_comp_isoCocycles₁_hom_apply, groupHomology.cyclesMk₁_eq, groupHomology.cyclesIso₀_comp_H0π_assoc, groupHomology.mapCycles₂_comp_i_assoc, groupCohomology.isoCocycles₁_hom_comp_i, groupHomology.instEpiModuleCatH0π, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, 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, groupCohomology.cochainsMap_f_hom, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, groupHomology.inhomogeneousChains.d_comp_d, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, groupHomology.π_comp_H0Iso_hom, groupCohomology.π_comp_H2Iso_hom_apply, HasLimit.lift_hom_apply, binaryProductLimitCone_isLimit_lift, groupHomology.cyclesIso₀_inv_comp_cyclesMap, groupHomology.H0π_comp_H0Iso_hom, 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, groupHomology.π_comp_H0IsoOfIsTrivial_hom_assoc, 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, Rep.instMonoModuleCatToModuleCatHom, groupCohomology.isoCocycles₁_inv_comp_iCocycles_assoc, groupCohomology.H1π_comp_H1IsoOfIsTrivial_hom, ofHom₂_compr₂, Rep.RepToAction_obj, groupHomology.d₁₀ArrowIso_hom_right, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_assoc, groupHomology.π_comp_H1Iso_inv_apply, groupHomology.cyclesIso₀_comp_H0π, 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.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, groupHomology.chainsMap_f_0_comp_chainsIso₀_apply, groupHomology.H0π_comp_H0Iso_hom_assoc, groupCohomology.H1π_comp_map, MonModuleEquivalenceAlgebra.inverse_map_hom, PresheafOfModules.ofPresheaf_map, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, groupCohomology.cocyclesMk₀_eq, groupHomology.lsingle_comp_chainsMap_f_assoc, ofHom_id, groupCohomology.isoShortComplexH1_inv, extendsScalars_map_leftUnitor_inv_one_tmul, mono_as_hom'_subtype, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, extendScalarsId_inv_app_apply, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d_assoc, sMulCommClass_mk, QuadraticModuleCat.moduleCat_of_toModuleCat, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, 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, groupHomology.H0π_comp_H0Iso_hom_apply, 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, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, groupCohomology.isoCocycles₁_hom_comp_i_assoc, groupHomology.mapCycles₁_quotientGroupMk'_epi, groupHomology.mapCycles₁_comp_i_assoc, groupHomology.H0π_comp_map_apply, 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.chainsMap_f_0_comp_chainsIso₀, groupHomology.H2π_eq_zero_iff, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, isSeparator, groupHomology.δ₁_apply, groupHomology.H1π_eq_iff, biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, CoextendScalars.map_apply, groupHomology.chainsMap_f, Profinite.NobelingProof.succ_mono, groupHomology.chainsMap_f_2_comp_chainsIso₂_apply, groupHomology.cyclesMap_comp_isoCycles₁_hom, groupCohomology.d₀₁_eq_zero
ofHom 📖	CompOp	94 math math: CategoryTheory.preadditiveCoyonedaObj_map, biproductIsoPi_inv_comp_π, CategoryTheory.linearCoyoneda_map_app, epi_as_hom''_mkQ, toMatrixModCat_map, ofHom_comp, CategoryTheory.linearYoneda_obj_map, CategoryTheory.ShortComplex.moduleCatMk_g, PresheafOfModules.restrictScalarsObj_map, LinearEquiv.toModuleIso_inv, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, HasLimit.productLimitCone_cone_π, QuadraticModuleCat.forget₂_map, RestrictionCoextensionAdj.counit'_app, MonoidalCategory.whiskerLeft_def, Profinite.NobelingProof.succ_exact, 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, cokernel_π_cokernelIsoRangeQuotient_hom, Rep.invariantsAdjunction_unit_app, lof_coprodIsoDirectSum_inv, CategoryTheory.linearYoneda_map_app, CoalgCat.comul_def, directLimitIsColimit_desc, smulShortComplex_g, biprodIsoProd_inv_comp_snd, range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, imageIsoRange_hom_subtype_assoc, TannakaDuality.FiniteGroup.equivApp_hom, MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, RestrictionCoextensionAdj.unit'_app, imageIsoRange_inv_image_ι, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, PresheafOfModules.homMk_app, groupCohomology.subtype_comp_d₀₁_assoc, groupHomology.lsingle_comp_chainsMap_f, imageIsoRange_inv_image_ι_assoc, 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, ι_coprodIsoDirectSum_hom, groupHomology.inhomogeneousChains.ext_iff, MonModuleEquivalenceAlgebra.inverseObj_mul, CategoryTheory.linearCoyoneda_obj_map, CoalgCat.forget₂_map, piIsoPi_hom_ker_subtype, Rep.forget₂_moduleCat_map, piIsoPi_inv_kernel_ι, extendScalars_η, uliftFunctor_map, ofHom_hom, ChainComplex.linearYonedaObj_d, directLimitCocone_ι_app, Hom.hom₂_apply, MatrixModCat.toModuleCat_map, binaryProductLimitCone_isLimit_lift, CategoryTheory.ShortComplex.moduleCatMk_f, AlgCat.forget₂_module_map, CoalgCat.toComon_map_hom, biprodIsoProd_inv_comp_fst, groupCohomology.subtype_comp_d₀₁, extendScalars_δ, ofHom₂_compr₂, hom_ofHom, extendScalars_ε, 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, monoidalClosed_pre_app, LinearEquiv.toModuleIso_hom, HasLimit.productLimitCone_isLimit_lift, semilinearMapAddEquiv_apply, extendScalars_μ, MonModuleEquivalenceAlgebra.inverseObj_one, ihom_ev_app, 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 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 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	DFunLike.coe LinearMap Ring.toSemiring RingHom.id Semiring.toNonAssocSemiring carrier AddCommGroup.toAddCommMonoid isAddCommGroup isModule LinearMap.instFunLike Hom.hom homMk CategoryTheory.Functor.obj ModuleCat moduleCategory AddCommGrpCat AddCommGrpCat.instCategory CategoryTheory.forget₂ instConcreteCategoryLinearMapIdCarrier AddMonoidHom AddCommGrpCat.carrier AddZeroClass.toAddZero AddMonoid.toAddZeroClass SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup AddCommGrpCat.str AddMonoidHom.instFunLike AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier hasForgetToAddCommGroup 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.toNSMul 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 SubNegMonoid.toAddMonoid AddGroup.toSubNegMonoid AddCommGroup.toAddGroup	—	—
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	187 math math: CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.ι_d, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, ModuleCat.hom_zero, Rep.invariantsAdjunction_homEquiv_symm_apply_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, 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, CompHausLike.LocallyConstantModule.functor_obj_obj_map_hom_apply_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, ModuleCat.endRingEquiv_symm_apply_hom, groupCohomology.mapCocycles₂_comp_i_apply, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, PresheafOfModules.Derivation.postcomp_d_apply, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, PresheafOfModules.pushforward_map_app_apply', groupCohomology.cocycles₁IsoOfIsTrivial_hom_hom_apply_apply, ModuleCat.MonoidalCategory.whiskerLeft_def, ModuleCat.hom_smul, 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, PresheafOfModules.Monoidal.tensorObj_map_tmul, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, ModuleCat.monoidalClosed_curry, ModuleCat.homAddEquiv_symm_apply_hom, ModuleCat.range_eq_top_of_epi, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, ModuleCat.hom_whiskerRight, ModuleCat.hom_inv_associator, FGModuleCat.hom_id, ModuleCat.directLimitIsColimit_desc, FDRep.hom_hom_action_ρ, PresheafOfModules.forgetToPresheafModuleCatObjMap_apply, groupHomology.mapCycles₁_comp_i_apply, ModuleCat.hom_whiskerLeft, 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, 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, Rep.ActionToRep_map, ModuleCat.hom_inv_rightUnitor, ModuleCat.hom_sum, groupHomology.π_comp_H1Iso_hom_apply, ModuleCat.hom_nsmul, groupHomology.chainsMap_id_f_hom_eq_mapRange, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, LinearMap.id_moduleCat_comp, 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, 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, FGModuleCat.hom_ext_iff, Rep.FiniteCyclicGroup.homResolutionIso_inv_f_hom_apply_hom_toFun, ModuleCat.hom_hom_associator, Rep.coinvariantsAdjunction_unit_app, 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, Rep.trivialFunctor_map_hom, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Rep.coinvariantsTensor_hom_ext_iff, ModuleCat.homMk_hom_apply, ModuleCat.hom_id, groupHomology.chainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_f'_hom, ModuleCat.uliftFunctor_map, groupCohomology.mapCocycles₁_comp_i_apply, ModuleCat.hom_zsmul, ModuleCat.ofHom_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, groupCohomology.cochainsMap_f_hom, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, MatrixModCat.toModuleCat_map, groupCohomology.π_comp_H2Iso_hom_apply, ModuleCat.HasLimit.lift_hom_apply, ModuleCat.binaryProductLimitCone_isLimit_lift, 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, 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, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, ModuleCat.homAddEquiv_apply, ModuleCat.span_rightExact, ModuleCat.endRingEquiv_apply, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, Rep.coinvariantsAdjunction_homEquiv_apply_hom, 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, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, FDRep.hom_action_ρ, ModuleCat.toKernelSubobject_arrow, CategoryTheory.Iso.toLinearMap_toLinearEquiv, CompHausLike.LocallyConstantModule.functor_map_hom_app_hom_apply_apply, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, groupHomology.π_comp_H2Iso_inv_apply, AlgebraicGeometry.tilde.instIsLocalizedModuleCarrierCarrierObjOppositeOpensCarrierCarrierCommRingCatSpecModuleCatPresheafModulesSheafModulesSpecToSheafOpBasicOpenPowersHomToOpen, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_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.of ModuleCat.instAddCommGroupHom instModule LinearMap.addCommGroup hom' 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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