ModuleCat

📁 Source: MathlibTest/CategoryTheory/ConcreteCategory/ModuleCat.lean

Statistics

Metric	Count
Definitions ModuleCat	1
Theorems	0
Total	1

(root)

Definitions

Name	Category	Theorems
ModuleCat 📖	CompData	1471 math math: ModuleCat.HasColimit.colimitCocone_pt_isAddCommGroup, ModuleCat.instIsRightAdjointCoextendScalars, ModuleCat.instPreservesMonomorphismsRestrictScalars, PresheafOfModules.Monoidal.tensorObj_obj, groupHomology.mapShortComplexH2_τ₁, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom_apply, groupCohomology.instEpiModuleCatH2π, groupCohomology.mapShortComplexH1_τ₂, ModuleCat.hom_zero, groupHomology.π_comp_H2Iso_hom_assoc, ModuleCat.instReflectsIsomorphismsForgetLinearMapIdCarrier, Rep.invariantsAdjunction_homEquiv_symm_apply_hom, LightCondensed.free_internallyProjective_iff_tensor_condition, CategoryTheory.linearCoyoneda_obj_additive, ModuleCat.instFullUliftFunctor, ModuleCat.forget_preservesLimits, ModuleCat.directLimitDiagram_obj_isModule, CommRingCat.KaehlerDifferential.map_d, CategoryTheory.preadditiveCoyonedaObj_map, ModuleCat.MonoidalCategory.braiding_hom_apply, ModuleCat.biproductIsoPi_inv_comp_π, simple_of_finrank_eq_one, ModuleCat.FilteredColimits.colimit_smul_mk_eq, groupHomology.mapCycles₂_comp_assoc, ModuleCat.restrictScalars.map_apply, Condensed.instAB4StarCondensedMod, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom, ModuleCat.forget₂_reflectsLimitsOfSize, CategoryTheory.additive_yonedaObj, groupCohomology.toCocycles_comp_isoCocycles₁_hom, CategoryTheory.linearCoyoneda_map_app, CategoryTheory.linearCoyoneda_obj_obj_carrier, ModuleCat.projective_of_free, groupCohomology.isoCocycles₁_hom_comp_i_apply, instEssentiallySmallFGModuleCat, groupHomology.map₁_quotientGroupMk'_epi, TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegular, MoritaEquivalence.linear, groupHomology.coinfNatTrans_app, ModuleCat.cokernel_π_ext, groupHomology.mapShortComplexH2_id, ModuleCat.forget_preservesLimitsOfSize, ModuleCat.restrictScalarsCongr_symm, LightCondensed.ihomPoints_apply, CategoryTheory.projectiveDimension_eq_of_semiLinearEquiv, LinearMap.id_fgModuleCat_comp, ModuleCat.restrictScalarsId'App_inv_naturality_assoc, groupHomology.d₁₀_single_one, groupHomology.shortComplexH1_f, FDRep.char_tensor, groupHomology.coinvariantsMk_comp_H0Iso_inv_apply, ModuleCat.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, ModuleCat.freeHomEquiv_apply, ModuleCat.epi_as_hom''_mkQ, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, ModuleCat.forget₂AddCommGroup_preservesLimitsOfSize, ModuleCat.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, ModuleCat.extendScalarsId_hom_app_one_tmul, groupCohomology.H1π_comp_map_assoc, ModuleCat.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, ModuleCat.ofHom_comp, groupHomology.H0IsoOfIsTrivial_inv_eq_π, groupCohomology.π_comp_H1Iso_hom_assoc, ModuleCat.ι_coprodIsoDirectSum_hom_apply, ModuleCat.restrictScalarsComp'App_hom_apply, PresheafOfModules.epi_iff_surjective, groupHomology.cyclesMap_id_comp, LightCondensed.ihomPoints_symm_comp, ModuleCat.isZero_iff_subsingleton, groupHomology.mapShortComplexH2_zero, groupCohomology.eq_d₁₂_comp_inv, CategoryTheory.whiskering_linearCoyoneda, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom_apply, CategoryTheory.ShortComplex.moduleCatMk_X₁_carrier, Condensed.instAB5CondensedMod, groupCohomology.instPreservesZeroMorphismsRepCochainComplexModuleCatNatCochainsFunctor, groupCohomology.mapCocycles₂_comp_i, PresheafOfModules.evaluation_preservesColimitsOfShape, ModuleCat.AlternatingMap.postcomp_apply, groupHomology.H1CoresCoinf_exact, groupHomology.eq_d₃₂_comp_inv, FGModuleCat.instHasColimitsOfShapeOfFinCategory, PresheafOfModules.comp_app, CategoryTheory.ShortComplex.moduleCatMk_X₁_isAddCommGroup, ModuleCat.localizedModuleFunctor_map, groupHomology.chainsMap_id, ModuleCat.linearIndependent_shortExact, instSmallUnitsSkeletonModuleCat, Rep.invariantsFunctor_obj_carrier, ModuleCat.monoidalClosed_uncurry, groupCohomology.H0IsoOfIsTrivial_hom, ModuleCat.matrixEquivalence_inverse, TannakaDuality.FiniteGroup.forget_obj, CondensedMod.isDiscrete_tfae, CategoryTheory.linearYoneda_obj_map, SheafOfModules.evaluationPreservesLimit, ModuleCat.hasLimits', CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, groupCohomology.coe_mapCocycles₁, SheafOfModules.forgetToSheafModuleCat_map_hom, ModuleCat.Iso.homCongr_eq_arrowCongr, ModuleCat.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, ModuleCat.directLimitCocone_pt_carrier, ModuleCat.toMatrixModCat_obj_carrier, ModuleCat.preservesFiniteLimits_extendScalars_of_flat, ModuleCat.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, ModuleCat.hasInjectiveDimensionLE_iff_forall_maximalSpectrum, LightCondMod.instPreservesEpimorphismsLightCondSetForget, ModuleCat.forget_preservesEpimorphisms, PresheafOfModules.Derivation.d_map, groupHomology.map_id, QuadraticModuleCat.forget₂_map_associator_inv, LinearMap.comp_id_fgModuleCat, ModuleCat.HasColimit.instHasColimit, ModuleCat.RestrictionCoextensionAdj.HomEquiv.toRestriction_hom_apply, groupCohomology.cochainsMap_comp, AlgebraicGeometry.tilde.map_sub, groupCohomology.comp_d₁₂_eq, ModuleCat.toMatrixModCat_obj_isAddCommGroup, groupHomology.δ₀_apply, groupCohomology.cocycles₂.d₂₃_apply, ModuleCat.extendRestrictScalarsAdj_homEquiv_apply, groupHomology.π_comp_H1Iso_inv, groupHomology.d₃₂_single_one_thd, CategoryTheory.ShortComplex.moduleCatMk_g, LightCondMod.isDiscrete_tfae, Rep.preservesLimits_forget, ModuleCat.restrictScalarsComp'_inv_app, ModuleCat.hom_tensorHom, groupHomology.isoCycles₁_inv_comp_iCycles_apply, groupHomology.coresNatTrans_app, ModuleCat.restrictScalars_η, PresheafOfModules.free_map_app, Rep.instIsEquivalenceModuleCatMonoidAlgebraOfModuleMonoidAlgebra, groupHomology.instPreservesZeroMorphismsRepModuleCatFunctor, ModuleCat.forget₂_addCommGrp_essSurj, groupCohomology.dArrowIso₀₁_inv_right, groupCohomology.map_H0Iso_hom_f_apply, ModuleCat.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, ModuleCat.enoughProjectives, ModuleCat.restrictScalarsId'App_hom_naturality, LinearEquiv.toModuleIso_inv, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, SheafOfModules.evaluationPreservesLimitsOfShape, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape, ModuleCat.exteriorPower.iso₀_hom_naturality, ModuleCat.forget_reflectsLimitsOfSize, instIsEquivalenceFGModuleCatUlift, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.toRestrictScalars_hom_apply, groupHomology.π_comp_H0Iso_hom_assoc, ModuleCat.restrictScalars_isEquivalence_of_ringEquiv, groupHomology.d₃₂_comp_d₂₁_assoc, CoalgCat.comonEquivalence_inverse, ModuleCat.endRingEquiv_symm_apply_hom, FGModuleCat.instFiniteHomModuleCatObjIsFG, ModuleCat.restrictScalarsComp'_hom_app, groupHomology.H1CoresCoinfOfTrivial_X₁, ModuleCat.extendRestrictScalarsAdj_counit_app_apply_one_tmul, groupHomology.chainsMap_id_f_map_mono, ModuleCat.FilteredColimits.colimit_zero_eq, groupCohomology.mapShortComplexH2_comp_assoc, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, ModuleCat.instPreservesFiniteLimitsLocalizationLocalizedModuleFunctor, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁_apply, ModuleCat.forget_preservesMonomorphisms, groupCohomology.mapCocycles₂_comp_i_apply, ModuleCat.instHasFiniteColimits, groupCohomology.cocyclesMap_comp_isoCocycles₂_hom_apply, ModuleCat.localizedModuleFunctor_obj, PresheafOfModules.id_app, CategoryTheory.IsGrothendieckAbelian.GabrielPopescu.full, ModuleCat.MonoidalCategory.associator_hom_apply, groupCohomology.cochainsMap_f_3_comp_cochainsIso₃_apply, groupHomology.d₁₀ArrowIso_hom_left, AlgebraicGeometry.instAdditiveModuleCatCarrierModulesSpecOfFunctor, groupHomology.cycles₁IsoOfIsTrivial_hom_apply, ModuleCat.HasLimit.productLimitCone_cone_π, ModuleCat.HasColimit.colimitCocone_ι_app, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_apply, PresheafOfModules.restrictScalarsObj_obj, instHasSeparatorModuleCatOfSmall, Rep.coinvariantsAdjunction_homEquiv_symm_apply_hom, ModuleCat.MonoidalCategory.tensorHom_tmul, groupHomology.d₂₁_single_inv_mul_ρ_add_single, QuadraticModuleCat.forget₂_map, postcomp_extClass_surjective_of_projective_X₂, groupCohomology.instMonoModuleCatFH1InfRes, ModuleCat.smulShortComplex_X₃_isAddCommGroup, ModuleCat.forget₂_addCommGroup_full, groupCohomology.cocyclesIso₀_inv_comp_iCocycles, ModuleCat.hasLimitsOfSize, PresheafOfModules.sectionsMap_coe, groupCohomology.mapCocycles₂_comp_i_assoc, groupHomology.d₁₀_comp_coinvariantsMk_apply, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_hom_apply, groupCohomology.H1IsoOfIsTrivial_inv_apply, groupHomology.π_comp_H2Iso_inv_assoc, ModuleCat.shortComplex_shortExact, ModuleCat.instPreservesFiniteColimitsUliftFunctor, PresheafOfModules.map_comp_apply, ModuleCat.biprodIsoProd_inv_comp_snd_apply, ModuleCat.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, ModuleCat.MonoidalCategory.whiskerLeft_def, groupCohomology.H2π_comp_map_apply, groupHomology.mapCycles₁_comp, Module.Flat.lTensor_shortComplex_exact, groupHomology.map_comp, ModuleCat.homLinearEquiv_symm_apply, Profinite.NobelingProof.succ_exact, ModuleCat.hom_smul, groupCohomology.dArrowIso₀₁_hom_right, FGModuleCat.instFiniteCarrierSigmaObjModuleCatOfFinite, ModuleCat.uliftFunctorForgetIso_hom_app, groupCohomology.π_map_assoc, CompHausLike.LocallyConstantModule.functorToPresheaves_map_app, ModuleCat.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, ModuleCat.imageIsoRange_hom_subtype, AlgebraicGeometry.isIso_fromTildeΓ_of_presentation, groupHomology.mapCycles₁_comp_i, ModuleCat.CoextendScalars.smul_apply, Rep.coinvariantsTensorIndIso_inv, groupCohomology.shortComplexH0_f, ModuleCat.binaryProductLimitCone_cone_π_app_right, groupCohomology.shortComplexH0_g, ModuleCat.exteriorPower.desc_mk, PresheafOfModules.unit_map_one, groupHomology.functor_obj, PresheafOfModules.zsmul_app, CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_hom, FDRep.instFiniteDimensionalHom, ModuleCat.matrixEquivalence_functor, ModuleCat.HasColimit.colimitCocone_pt_isModule, Rep.ActionToRep_obj_V, groupCohomology.shortComplexH1_f, ModuleCat.hasLimits, CategoryTheory.preadditiveYoneda_obj, CategoryTheory.linearCoyoneda_obj_obj_isAddCommGroup, CategoryTheory.Abelian.Pseudoelement.ModuleCat.eq_range_of_pseudoequal, Rep.standardComplex.εToSingle₀_comp_eq, ModuleCat.MonoidalCategory.tensorHom_def, groupHomology.inhomogeneousChains.d_def, PresheafOfModules.isoMk_hom_app, Rep.instEpiModuleCatAppCoinvariantsMk, CommRingCat.moduleCatRestrictScalarsPseudofunctor_mapId, ModuleCat.restrictScalarsId'App_inv_naturality, groupCohomology.H1IsoOfIsTrivial_H1π_apply_apply, ModuleCat.imageIsoRange_inv_image_ι_apply, CategoryTheory.preadditiveYonedaMap_app, groupCohomology.comp_d₂₃_eq, CondensedMod.isDiscrete_iff_isDiscrete_forget, PresheafOfModules.map_smul, FGModuleCat.FGModuleCatEvaluation_apply, ModuleCat.epi_iff_surjective, ModuleCat.restrictScalarsId'_inv_app, AlgebraicGeometry.instFullModuleCatCarrierModulesSpecOfFunctor, PresheafOfModules.Monoidal.tensorObj_map_tmul, ModuleCat.exteriorPower.map_mk, ModuleCat.cokernel_π_cokernelIsoRangeQuotient_hom, ModuleCat.extendScalars_assoc_assoc, groupHomology.H1CoresCoinf_X₁, Rep.ofModuleMonoidAlgebra_obj_coe, ModuleCat.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, ModuleCat.hom_inv_apply, groupHomology.mapCycles₂_id_comp, CategoryTheory.ShortComplex.moduleCatMk_X₃_isAddCommGroup, CondensedMod.LocallyConstant.instFullModuleCatCondensedDiscrete, ModuleCat.monoidalClosed_curry, groupCohomology.d₀₁_apply_mem_cocycles₁, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc, ModuleCat.exteriorPower.iso₁_hom_naturality, ModuleCat.hasColimitsOfSize, PresheafOfModules.instPreservesLimitsOfSizeModuleCatCarrierObjOppositeRingCatEvaluation, Module.Flat.iff_rTensor_preserves_shortComplex_exact, groupHomology.cyclesMap_comp_assoc, ModuleCat.MonoidalCategory.leftUnitor_hom_apply, CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj, ModuleCat.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, ModuleCat.restrictScalarsId'App_hom_apply, groupCohomology.π_comp_H0IsoOfIsTrivial_hom, groupCohomology.subtype_comp_d₀₁_apply, SheafOfModules.pushforwardComp_inv_app_val_app, ModuleCat.ExtendRestrictScalarsAdj.Counit.map_apply_one_tmul, LightCondensed.internallyProjective_iff_tensor_condition, CategoryTheory.projectiveDimension_eq_of_linearEquiv, ModuleCat.FilteredColimits.forget_preservesFilteredColimits, ModuleCat.cokernel_π_imageSubobject_ext, groupCohomology.H2π_eq_iff, CoalgCat.toComonObj_X, groupCohomology.cochainsMap_f_map_epi, groupCohomology.comp_d₀₁_eq, ModuleCat.forget₂_map_homMk, FGModuleCat.instIsMonoidalClosedModuleCatIsFG, ModuleCat.instPreservesInjectiveObjectsLocalizationLocalizedModuleFunctorOfIsNoetherianRing, Rep.instFaithfulModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, ModuleCat.restrictScalarsId'App_hom_naturality_assoc, groupCohomology.δ₁_apply, ModuleCat.homAddEquiv_symm_apply_hom, LinearMap.shortExact_shortComplexKer, groupHomology.coinvariantsMk_comp_H0Iso_inv, ModuleCat.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, ModuleCat.ExtendScalars.map'_id, PresheafOfModules.freeObj_map, SheafOfModules.instSmallElemForallObjCompModuleCatCarrierOppositeRingCatObjFunctorIsSheafPresheafOfModulesForgetEvaluationForgetLinearMapIdCarrierSections, FGModuleCat.instFiniteHom, groupCohomology.cochainsMap_zero, ModuleCat.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, ModuleCat.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, ModuleCat.hom_whiskerRight, Rep.instAdditiveModuleCatObjFunctorCoinvariantsTensor, ModuleCat.hom_inv_associator, PresheafOfModules.instEpiModuleCatCarrierObjOppositeRingCatApp, FGModuleCat.hom_id, groupCohomology.H1InfRes_X₂, ModuleCat.lof_coprodIsoDirectSum_inv, LightCondMod.LocallyConstant.instFullModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, groupCohomology.map₁_one, ModuleCat.localizedModule_hasProjectiveDimensionLE, CategoryTheory.linearYoneda_map_app, instAB4ModuleCat, CommRingCat.moduleCatRestrictScalarsPseudofunctor_map, CoalgCat.comul_def, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i, ModuleCat.inv_hom_apply, ModuleCat.forget₂AddCommGroup_preservesLimits, CategoryTheory.Abelian.full_comp_preadditiveCoyonedaObj, ModuleCat.directLimitIsColimit_desc, CategoryTheory.preadditiveYonedaObj_obj_isModule, groupHomology.mapCycles₁_id_comp_apply, ModuleCat.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, ModuleCat.smulShortComplex_g, ModuleCat.directLimitCocone_pt_isAddCommGroup, precomp_extClass_surjective_of_projective_X₂, groupCohomology.map_id, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.full_embedding, groupCohomology.mapShortComplexH2_comp, ModuleCat.ExtendScalars.map'_comp, groupCohomology.shortComplexH2_f, CategoryTheory.linearYoneda_obj_obj_isAddCommGroup, simple_iff_isSimpleModule, Rep.RepToAction_map_hom, ModuleCat.restrictScalarsComp'App_hom_naturality_assoc, groupCohomology.instEpiModuleCatH1π, ModuleCat.MonoidalCategory.associator_def, groupHomology.H1CoresCoinfOfTrivial_X₂, groupHomology.H1CoresCoinf_X₂, IsProjective.iff_projective, groupCohomology.H2π_comp_map, groupCohomology.cochainsMap_comp_assoc, TopModuleCat.instIsRightAdjointModuleCatIndiscrete, FGModuleCat.instFiniteCarrierLimitModuleCatCompForget₂LinearMapIdObjIsFG, ModuleCat.mono_iff_injective, groupHomology.π_comp_H2Iso_hom, ModuleCat.forget₂_obj, CategoryTheory.Injective.injective_iff_preservesEpimorphisms_preadditive_yoneda_obj', TopModuleCat.instIsLeftAdjointModuleCatWithModuleTopology, FDRep.hom_hom_action_ρ, ModuleCat.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, ModuleCat.hom_whiskerLeft, groupHomology.chainsMap_f_map_epi, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, AlgCat.forget₂Module_preservesLimitsOfSize, groupHomology.mapCycles₂_comp, ModuleCat.comp_apply, ModuleCat.instPreservesProjectiveObjectsLocalizationLocalizedModuleFunctor, ModuleCat.restrictScalarsCongr_hom_app, ModuleCat.MonoidalCategory.tensorUnit_carrier, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, groupHomology.isoShortComplexH1_hom, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars_hom_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap_apply, CategoryTheory.whiskering_linearYoneda, ModuleCat.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, ModuleCat.FilteredColimits.M.mk_map, groupCohomology.π_comp_H0Iso_hom_apply, ModuleCat.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, ModuleCat.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, ModuleCat.MonoidalCategory.tensorLift_tmul, simple_of_isSimpleModule, MatrixModCat.toModuleCat_obj_carrier, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_assoc, ModuleCat.hom_hom_leftUnitor, groupHomology.chainsFunctor_obj, groupCohomology.mapCocycles₁_one, PresheafOfModules.surjective_of_epi, groupCohomology.instMonoModuleCatFShortComplexH0, FGModuleCat.instFiniteCarrierPiObjModuleCatOfFinite, ModuleCat.adj_homEquiv, groupCohomology.functor_obj, groupCohomology.cocyclesMap_comp, CategoryTheory.preservesFiniteColimits_preadditiveYonedaObj_of_injective, groupHomology.H2π_comp_map_assoc, AlgebraicGeometry.tilde.map_comp_assoc, ModuleCat.hom_hom_rightUnitor, ModuleCat.biprodIsoProd_inv_comp_snd, groupHomology.π_comp_H0IsoOfIsTrivial_hom_apply, ModuleCat.piIsoPi_inv_kernel_ι_apply, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_zero_apply, ModuleCat.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, ModuleCat.instIsLeftAdjointRestrictScalars, ModuleCat.lof_coprodIsoDirectSum_inv_apply, Condensed.instIsRightKanExtensionFintypeCatCondensedModProfiniteProfiniteSolidProfiniteSolidCounit, groupHomology.d₁₀ArrowIso_inv_right, ModuleCat.Derivation.desc_d, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv, TannakaDuality.FiniteGroup.equivApp_inv, QuadraticModuleCat.forget₂_map_associator_hom, ModuleCat.exteriorPower.iso₀_hom_naturality_assoc, groupCohomology.resNatTrans_app, PresheafOfModules.injective_of_mono, ModuleCat.free_ε_one, PresheafOfModules.isoMk_inv_app, groupCohomology.π_comp_H0Iso_hom_assoc, groupCohomology.π_map, CategoryTheory.full_linearCoyoneda, TannakaDuality.FiniteGroup.forget_map, ModuleCat.MonModuleEquivalenceAlgebra.functor_obj_carrier, ModuleCat.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, ModuleCat.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, ModuleCat.smulNatTrans_apply_app, FGModuleCat.ihom_obj, groupCohomology.cochainsMap_id_f_map_mono, CoalgCat.comonEquivalence_functor, groupHomology.chainsMap_id_comp, ModuleCat.forget_reflectsLimits, TannakaDuality.FiniteGroup.equivApp_hom, ModuleCat.uliftFunctorForgetIso_inv_app, FDRep.char_linHom, groupHomology.instEpiModuleCatGH1CoresCoinf, groupCohomology.mapShortComplexH1_id, CommRingCat.moduleCatExtendScalarsPseudofunctor_map, groupHomology.H2π_eq_iff, FGModuleCat.instAdditiveModuleCatForget₂LinearMapIdCarrierObjIsFG, ModuleCat.reflectsIsomorphisms_extendScalars_of_faithfullyFlat, ModuleCat.ExtendRestrictScalarsAdj.homEquiv_symm_apply, groupHomology.H1AddEquivOfIsTrivial_single, LightCondMod.instReflectsEpimorphismsLightCondSetForget, CategoryTheory.preservesFiniteColimits_preadditiveCoyonedaObj_of_projective, groupHomology.mapShortComplexH1_id_comp, CoalgCat.ofComonObjCoalgebraStruct_comul, ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, groupHomology.mapShortComplexH1_comp, PresheafOfModules.unitHomEquiv_apply_coe, groupCohomology.inhomogeneousCochains.d_comp_d, ModuleCat.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, ModuleCat.RestrictionCoextensionAdj.unit'_app, ModuleCat.matrixEquivalence_unitIso, groupHomology.eq_d₂₁_comp_inv_assoc, ModuleCat.imageIsoRange_inv_image_ι, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom, ModuleCat.smulShortComplex_X₃_carrier, RingCat.moduleCatRestrictScalarsPseudofunctor_mapId, ModuleCat.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, ModuleCat.Algebra.instLinearRestrictScalars, groupHomology.inhomogeneousChains.d_single, groupCohomology.mapShortComplexH2_τ₁, Rep.ActionToRep_map, FGModuleRepr.instIsEquivalenceFGModuleCatEmbed, groupHomology.cyclesIso₀_inv_comp_iCycles, ModuleCat.instReflectsIsomorphismsRestrictScalars, ModuleCat.exteriorPower.iso₁_hom_apply, FGModuleCat.instHasFiniteColimits, groupCohomology.d₁₂_comp_d₂₃_assoc, ModuleCat.uliftFunctor_map_exact, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_map, SheafOfModules.pushforwardPushforwardAdj_unit_app_val_app, PresheafOfModules.evaluation_preservesLimit, ModuleCat.hom_inv_rightUnitor, ModuleCat.ExtendScalars.smul_tmul, LightCondensed.free_internallyProjective_iff_tensor_condition', groupHomology.map_id_comp_H0Iso_hom_assoc, instHasLimitsOfSizeCondensedMod, ModuleCat.hom_sum, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_mon, Rep.RepToAction_obj_V_carrier, ModuleCat.restrictScalarsComp'App_hom_naturality, QuadraticModuleCat.forget₂_obj, FGModuleCat.instFiniteCarrierColimitModuleCatCompForget₂LinearMapIdObjIsFG, groupCohomology.cochainsMap_f_2_comp_cochainsIso₂_apply, Rep.RepToAction_obj_V_isModule, ModuleCat.extendsScalars_map_rightUnitor_inv_one_tmul, CommRingCat.moduleCatExtendScalarsPseudofunctor_obj, ModuleCat.extendScalars_δ_tmul, groupCohomology.mapShortComplexH2_id_comp_assoc, groupHomology.mapCycles₂_id_comp_assoc, groupHomology.π_comp_H1Iso_hom_apply, ModuleCat.hom_nsmul, groupHomology.mapShortComplexH2_comp, groupCohomology.map_id_comp_H0Iso_hom_apply, ModuleCat.forget_obj, ModuleCat.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, ModuleCat.HasColimit.instPreservesColimitAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, groupHomology.mapShortComplexH2_τ₂, groupHomology.mapCycles₁_id_comp, Rep.trivialFunctor_obj_V, ModuleCat.FilteredColimits.forget₂AddCommGroup_preservesFilteredColimits, ModuleCat.instIsRightAdjointForgetLinearMapIdCarrier, ModuleCat.homEquiv_extendScalarsComp, ModuleCat.restrictScalars_μ_tmul, groupCohomology.cocycles₁IsoOfIsTrivial_inv_hom_apply_coe, QuadraticModuleCat.toModuleCat_tensor, ModuleCat.ExtendScalars.map_tmul, ModuleCat.FilteredColimits.colimit_add_mk_eq', PresheafOfModules.map_comp, Rep.preservesColimits_forget, ModuleCat.FilteredColimits.forget_reflectsFilteredColimits, CompHausLike.LocallyConstantModule.functor_obj_obj_obj_isAddCommGroup_neg_apply, RingCat.moduleCatRestrictScalarsPseudofunctor_map, groupHomology.chainsMap_f_map_mono, LinearMap.id_moduleCat_comp, ModuleCat.restrictScalarsComp'App_inv_naturality, ModuleCat.free_μ_freeMk_tmul_freeMk, ModuleCat.forget₂_obj_moduleCat_of, groupHomology.shortComplexH0_f, groupHomology.eq_d₁₀_comp_inv, CategoryTheory.Iso.toLinearEquiv_apply, FDRep.instHasKernels, ModuleCat.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, ModuleCat.MonoidalCategory.tensorObj, ModuleCat.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, ModuleCat.instPreservesColimitsOfSizeAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrierOfHasColimitsOfSizeAddCommGrpMax, ModuleCat.hasCokernels_moduleCat, groupCohomology.cocyclesIso₀_hom_comp_f_assoc, groupHomology.lsingle_comp_chainsMap_f, ModuleCat.FreeMonoidal.μIso_hom_freeMk_tmul_freeMk, groupHomology.coinvariantsMk_comp_opcyclesIso₀_inv_apply, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, ModuleCat.imageIsoRange_inv_image_ι_assoc, ModuleCat.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, ModuleCat.binaryProductLimitCone_cone_π_app_left, ModuleCat.HasColimit.coconePointSMul_apply, PresheafOfModules.pushforward_obj_obj, Rep.instLinearModuleCatInvariantsFunctor, groupHomology.d₂₁_single_self_inv_ρ_sub_inv_self, ModuleCat.kernelIsoKer_hom_ker_subtype, ModuleCat.projective_of_categoryTheory_projective, ModuleCat.smulShortComplex_f, SheafOfModules.Presentation.mapRelations_mapGenerators, ModuleCat.hasLimitsOfShape, groupHomology.chainsMap_f_3_comp_chainsIso₃_assoc, ModuleCat.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, ModuleCat.MonoidalCategory.leftUnitor_inv_apply, groupCohomology.map_id_comp_assoc, ModuleCat.ι_coprodIsoDirectSum_hom, ModuleCat.instReflectsIsomorphismsAddCommGrpCatForget₂LinearMapIdCarrierAddMonoidHomCarrier, SheafOfModules.relationsOfIsCokernelFree_I, ModuleCat.MonModuleEquivalenceAlgebra.algebraMap, FDRep.instInjectiveOfNeZeroCastCard, ModuleCat.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, ModuleCat.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, ModuleCat.MonoidalCategory.tensorObj_isAddCommGroup, groupHomology.d₂₁_apply_mem_cycles₁, ModuleCat.ihom_map_apply, LightCondMod.LocallyConstant.instFaithfulModuleCatLightCondensedDiscrete, ModuleCat.instAdditiveRestrictScalars, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_mul, ModuleCat.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, ModuleCat.instAdditiveUliftFunctor, TannakaDuality.FiniteGroup.sumSMulInv_single_id, PresheafOfModules.Hom.naturality_assoc, groupCohomology.H1π_comp_map_apply, ModuleCat.free_shortExact, groupHomology.eq_d₃₂_comp_inv_assoc, ModuleCat.projectiveDimension_le_projectiveDimension_of_isLocalizedModule, groupCohomology.cocyclesMap_cocyclesIso₀_hom_f, ModuleCat.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, ModuleCat.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, ModuleCat.range_mkQ_cokernelIsoRangeQuotient_inv_apply, groupHomology.isoCycles₂_inv_comp_iCycles_assoc, ModuleCat.mkOfSMul_smul, groupCohomology.instPreservesZeroMorphismsRepModuleCatFunctor, groupHomology.isoShortComplexH2_hom, LightCondMod.LocallyConstant.instFaithfulModuleCatFunctor, ModuleCat.instMonoι, groupHomology.mapShortComplex₂_exact, ModuleCat.restrictScalars.smul_def, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, ModuleCat.exteriorPower.iso₁_hom_naturality_assoc, CategoryTheory.preadditiveYonedaObj_obj_isAddCommGroup, groupHomology.cyclesMk₂_eq, groupHomology.chainsMap_f_1_comp_chainsIso₁, ModuleCat.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, ModuleCat.hasProjectiveDimensionLE_iff_forall_primeSpectrum, groupHomology.d₂₁_single_one_fst, SheafOfModules.unitToPushforwardObjUnit_val_app_apply, ModuleCat.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, ModuleCat.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, ModuleCat.instFaithfulUliftFunctor, groupHomology.H1π_comp_map_assoc, groupCohomology.map_id_comp, groupHomology.instEpiModuleCatH1π, Rep.instAdditiveModuleCatForget₂IntertwiningMapVρLinearMapIdCarrier, ModuleCat.piIsoPi_hom_ker_subtype_apply, ModuleCat.reflectsColimitsOfShape, FGModuleCat.instHasLimitsOfShapeOfFinCategory, RingCat.moduleCatRestrictScalarsPseudofunctor_obj, ModuleCat.MonoidalCategory.whiskerRight_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles, CondensedMod.LocallyConstant.instIsIsoCondensedSetMapForgetAppCondensedModuleCatCounitDiscreteUnderlyingAdjObjFunctor, Rep.coinvariantsTensor_hom_ext_iff, ModuleCat.homMk_hom_apply, ModuleCat.instPreservesLimitsOfSizeUliftFunctor, ModuleCat.free_δ_freeMk, FGModuleCat.instFullUlift, ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize, PresheafOfModules.instMonoModuleCatCarrierObjOppositeRingCatApp, ModuleCat.linearIndependent_leftExact, FDRep.instPreservesFiniteColimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, ModuleCat.instAdditiveLocalizationLocalizedModuleFunctor, ModuleCat.FilteredColimits.ι_colimitDesc, groupCohomology.δ₀_apply, ModuleCat.hasProjectiveDimensionLE_iff_forall_maximalSpectrum, CoalgCat.forget₂_map, Rep.unit_iso_comm, ModuleCat.restrictScalarsEquivalenceOfRingEquiv_additive, inhomogeneousCochains.d_eq, ModuleCat.HasLimit.productLimitCone_cone_pt_carrier, groupHomology.instEpiModuleCatH2π, groupHomology.H1CoresCoinfOfTrivial_exact, MoritaEquivalence.instAdditiveModuleCatFunctorEqv, ModuleCat.piIsoPi_hom_ker_subtype, ModuleCat.directLimitDiagram_obj_carrier, groupHomology.chainsFunctor_map, groupHomology.mapShortComplex₁_exact, ModuleCat.hom_id, groupCohomology.cocyclesMk₂_eq, LightCondMod.LocallyConstant.instFaithfulModuleCatSheafLightProfiniteCoherentTopologyConstantSheaf, ModuleCat.extendScalars_id_comp_assoc, ModuleCat.injectiveDimension_le_injectiveDimension_of_isLocalizedModule, groupHomology.instPreservesZeroMorphismsRepChainComplexModuleCatNatChainsFunctor, ModuleCat.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, ModuleCat.MonoidalCategory.tensorUnit_isModule, ModuleCat.extendScalars_assoc', ModuleCat.piIsoPi_inv_kernel_ι, LightCondMod.LocallyConstant.instFullModuleCatFunctor, ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.evalAt_apply, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, TopModuleCat.instIsLeftAdjointModuleCatForget₂ContinuousLinearMapIdCarrierLinearMap, ModuleCat.extendScalars_η, ModuleCat.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, ModuleCat.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, ModuleCat.wellPowered_moduleCat, FGModuleCat.tensorObj_obj, FGModuleCat.tensorUnit_obj, ModuleCat.FreeMonoidal.μIso_inv_freeMk, ModuleCat.uliftFunctor_map, groupHomology.functor_map, groupHomology.instEpiModuleCatH0π, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀, groupCohomology.H1InfRes_exact, ModuleCat.instPreservesFiniteLimitsUliftFunctor, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isAddCommGroup, groupCohomology.mapShortComplexH2_τ₂, groupCohomology.mapCocycles₁_comp_i_apply, ModuleCat.hom_zsmul, instHasFiniteLimitsLightCondMod, groupHomology.mapCycles₂_id_comp_apply, ChainComplex.linearYonedaObj_d, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc, ModuleCat.finite_ext, ModuleCat.ExtendRestrictScalarsAdj.counit_app, ModuleCat.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, ModuleCat.Hom.hom₂_apply, ModuleCat.HasColimit.colimitCocone_pt_carrier, CondensedMod.epi_iff_locallySurjective_on_compHaus, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, ModuleCat.uliftFunctor_obj, ModuleCat.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, ModuleCat.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, ModuleCat.instFaithfulRestrictScalars, MatrixModCat.toModuleCat_map, groupHomology.π_comp_H0Iso_hom, PresheafOfModules.map_id, CommRingCat.moduleCatExtendScalarsPseudofunctor_mapComp, ModuleCat.MonoidalCategory.leftUnitor_def, groupCohomology.mapShortComplexH1_id_comp_assoc, groupCohomology.π_comp_H2Iso_hom_apply, ModuleCat.HasLimit.lift_hom_apply, groupCohomology.mapShortComplexH1_zero, ModuleCat.binaryProductLimitCone_isLimit_lift, IsSMulRegular.smulShortComplex_shortExact, CategoryTheory.ShortComplex.moduleCatMk_f, ModuleCat.homLinearEquiv_apply, groupCohomology.mapShortComplexH1_comp_assoc, Rep.coinvariantsTensorMk_apply, groupHomology.cyclesIso₀_inv_comp_cyclesMap, FGModuleCat.FGModuleCatDual_coe, instHasLimitsOfSizeLightCondMod, ModuleCat.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, ModuleCat.FilteredColimits.M.mk_surjective, FDRep.forget₂_ρ, ModuleCat.extendScalarsComp_hom_app_one_tmul, Rep.invariantsFunctor_map_hom, ModuleCat.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, ModuleCat.MonoidalCategory.tensorObj_def, AlgebraicGeometry.tilde.map_zero, ModuleCat.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, ModuleCat.biprodIsoProd_inv_comp_fst, groupHomology.π_map_apply, CategoryTheory.Abelian.FreydMitchell.instFullModuleCatEmbeddingRingFunctor, ModuleCat.instIsLeftAdjointExtendScalars, groupHomology.d₃₂_comp_d₂₁, groupHomology.d₃₂_single_one_snd, groupHomology.instEpiModuleCatGShortComplexH0, CategoryTheory.IsGrothendieckAbelian.instIsLeftAdjointModuleCatMulOppositeEndTensorObj, ModuleCat.extendScalars_comp_id_assoc, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, SheafOfModules.relationsOfIsCokernelFree_s, ModuleCat.forget₂_reflectsLimits, FDRep.Iso.conj_ρ, FDRep.of_ρ, ModuleCat.forget₂PreservesColimitsOfShape, CondensedMod.instHasLimitsOfSizeModuleCat, MatrixModCat.toModuleCat_obj_isAddCommGroup, SheafOfModules.forgetToSheafModuleCat_obj_obj, Rep.coinvariantsTensorIndHom_mk_tmul_indVMk, ModuleCat.biproductIsoPi_inv_comp_π_apply, ModuleCat.shortComplex_exact, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, CondensedMod.LocallyConstant.instFaithfulModuleCatFunctor, ModuleCat.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, ModuleCat.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', ModuleCat.forget₂AddCommGroup_reflectsLimit, groupHomology.isoShortComplexH2_inv, groupHomology.coe_mapCycles₁, groupHomology.toCycles_comp_isoCycles₁_hom, ModuleCat.HasLimit.productLimitCone_cone_pt_isAddCommGroup, ModuleCat.hom_inv_leftUnitor, groupCohomology.d₀₁_comp_d₁₂_apply, Module.Flat.instPreservesFiniteLimitsModuleCatTensorLeftOfCarrier, ModuleCat.free_map_apply, groupHomology.chainsMap_f_2_comp_chainsIso₂_assoc, groupHomology.mapCycles₂_comp_i_apply, ModuleCat.binaryProductLimitCone_cone_pt, LightCondMod.LocallyConstant.instHasSheafifyLightProfiniteCoherentTopologyModuleCat, AlgebraicGeometry.tilde.functor_obj, groupCohomology.cocyclesIso₀_hom_comp_f_apply, ModuleCat.ofHom₂_hom_apply_hom, SheafOfModules.pushforwardPushforwardAdj_counit_app_val_app, groupCohomology.subtype_comp_d₀₁, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_carrier, groupCohomology.iCocycles_mk, groupHomology.isoCycles₂_hom_comp_i, ModuleCat.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, ModuleCat.extendScalars_δ, groupCohomology.π_map_apply, LightCondensed.instCountableAB4StarLightCondMod, ModuleCat.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, ModuleCat.localizedModuleFunctor_map_exact, ModuleCat.instHasLimitsOfSize, ModuleCat.ofHom₂_compr₂, CategoryTheory.hasProjectiveDimensionLE_of_linearEquiv, LightCondMod.LocallyConstant.instFullModuleCatLightCondensedDiscrete, ModuleCat.extendScalars_comp_id, PresheafOfModules.freeYonedaEquiv_comp, ModuleCat.forget₂AddCommGroup_preservesLimit, ModuleCat.hasKernels_moduleCat, groupHomology.shortComplexH0_g, Rep.RepToAction_obj, CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_iff, ModuleCat.FreeMonoidal.εIso_hom_one, CategoryTheory.preadditiveCoyonedaObj_obj_carrier, groupCohomology.mapShortComplexH2_id, groupHomology.d₁₀ArrowIso_hom_right, groupCohomology.shortComplexH0_exact, ModuleCat.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, ModuleCat.extendRestrictScalarsAdj_unit_app_apply, ModuleCat.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, ModuleCat.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, ModuleCat.MonoidalCategory.whiskerLeft_apply, PresheafOfModules.Finite.evaluation_preservesFiniteColimits, groupHomology.cyclesMk₀_eq, groupHomology.isoCycles₁_hom_comp_i, groupCohomology.cocyclesIso₀_inv_comp_iCocycles_apply, groupCohomology.shortComplexH2_g, ModuleCat.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', ModuleCat.smulShortComplex_X₃_isModule, TannakaDuality.FiniteGroup.map_mul_toRightFDRepComp, ModuleCat.MonModuleEquivalenceAlgebra.inverse_map_hom, ModuleCat.homAddEquiv_apply, PresheafOfModules.ofPresheaf_map, ModuleCat.MonModuleEquivalenceAlgebra.inverse_obj_X_isModule, ModuleCat.hasLimit, CategoryTheory.preservesLimits_preadditiveCoyonedaObj, ModuleCat.instPreservesProjectiveObjectsUliftFunctorOfSmall, groupHomology.epi_map_0_of_epi, groupHomology.mapShortComplexH1_τ₃, ModuleCat.directLimitCocone_pt_isModule, ModuleCat.span_rightExact, ModuleCat.instLinearUliftFunctor, CommRingCat.KaehlerDifferential.ext_iff, AlgebraicGeometry.instIsIsoFunctorModuleCatCarrierUnitModulesSpecOfAdjunction, groupHomology.cyclesMap_comp_cyclesIso₀_hom_assoc, groupCohomology.cocyclesMk₀_eq, AlgebraicGeometry.tilde.map_neg, FDRep.instPreservesFiniteLimitsRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρOfIsNoetherianRing, ModuleCat.endRingEquiv_apply, groupHomology.lsingle_comp_chainsMap_f_assoc, ModuleCat.directLimitDiagram_map, ModuleCat.ofHom_id, LightCondensed.instIsGrothendieckAbelianLightCondMod, ModuleCat.HasColimit.reflectsColimit, PresheafOfModules.naturality_apply, groupCohomology.isoShortComplexH1_inv, ModuleCat.image.fac, CategoryTheory.additive_coyonedaObj, ModuleCat.extendsScalars_map_leftUnitor_inv_one_tmul, LightCondMod.isDiscrete_iff_isDiscrete_forget, ModuleCat.mono_as_hom'_subtype, groupHomology.cyclesIso₀_inv_comp_iCycles_assoc, ModuleCat.FilteredColimits.ι_colimitDesc_assoc, ModuleCat.extendScalarsId_inv_app_apply, ModuleCat.semilinearMapAddEquiv_symm_apply_apply, ModuleCat.hasColimitsOfShape, groupCohomology.cochainsMap_id_f_hom_eq_compLeft, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc, Rep.coinvariantsAdjunction_homEquiv_apply_hom, PresheafOfModules.fromFreeYonedaCoproduct_app_mk, ModuleCat.hom_comp, ModuleCat.MonoidalCategory.braiding_inv_apply, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_inv_f_hom_apply, groupHomology.H1CoresCoinf_f, AlgebraicGeometry.structurePresheafInModuleCat_obj_carrier, ModuleCat.hom_neg, FDRep.scalar_product_char_eq_finrank_equivariant, instInvertibleCarrierOutModuleCatValSkeleton, groupCohomology.cochainsMap_f_1_comp_cochainsIso₁, ModuleCat.MonoidalCategory.whiskerRight_def, AlgebraicGeometry.isIso_fromTildeΓ_iff, FGModuleCat.instFaithfulUlift, groupCohomology.cochainsMap_id_comp_assoc, ModuleCat.preservesLimit_restrictScalars, groupCohomology.cochainsMap_f_0_comp_cochainsIso₀_assoc, groupCohomology.map_H0Iso_hom_f_assoc, ModuleCat.ofHom_apply, CategoryTheory.ShortComplex.Exact.moduleCat_of_range_eq_ker, TannakaDuality.FiniteGroup.ofRightFDRep_hom, CommRingCat.moduleCatRestrictScalarsPseudofunctor_obj, LightCondensed.instEpiLightCondModMapNat, ModuleCat.kernelIsoKer_inv_kernel_ι, Rep.coinvariantsTensorIndInv_mk_tmul_indMk, AlgebraicGeometry.tilde.map_id_assoc, simple_iff_isSimpleModule', groupHomology.shortComplexH1_g, Rep.instPreservesZeroMorphismsModuleCatCoinvariantsFunctor, ModuleCat.restrictScalarsCongr_inv_app, groupCohomology.eq_d₁₂_comp_inv_assoc, groupHomology.cyclesMap_id, ModuleCat.projectiveDimension_eq_iSup_localizedModule_prime, CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.preservesFiniteColimits_embedding, groupCohomology.H1InfRes_f, Rep.instAdditiveModuleCatInvariantsFunctor, ModuleCat.imageIsoRange_hom_subtype_apply, LinearMap.comp_id_moduleCat, CondensedMod.LocallyConstant.instFaithfulModuleCatSheafCompHausCoherentTopologyConstantSheaf, FDRep.instFaithfulRepForget₂HomSubtypeFGModuleCatLinearMapIdCarrierObjModuleCatIsFGVIntertwiningMapVρ, FGModuleCat.Iso.conj_hom_eq_conj, ModuleCat.smulShortComplex_X₂, MatrixModCat.toModuleCat_obj_isModule, ModuleCat.epi_iff_range_eq_top, instFreeCarrierX₂ModuleCatProjectiveShortComplex, ModuleCat.forget₂AddCommGroupIsEquivalence, groupHomology.d₁₀ArrowIso_inv_left, ModuleCat.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, ModuleCat.HasLimit.productLimitCone_isLimit_lift, ModuleCat.injectiveDimension_eq_iSup_localizedModule_maximal, ModuleCat.MonoidalCategory.tensorObj_carrier, isZero_groupHomology_succ_of_subsingleton, groupCohomology.isoShortComplexH2_inv, ModuleCat.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, ModuleCat.semilinearMapAddEquiv_apply, ModuleCat.CoextendScalars.map'_hom_apply_apply, TannakaDuality.FiniteGroup.equivHom_surjective, ModuleCat.RestrictionCoextensionAdj.HomEquiv.fromRestriction_hom_apply_apply, ModuleCat.freeHomEquiv_symm_apply, ModuleCat.ulift_injective_of_injective, CategoryTheory.preadditiveCoyonedaObj_obj_isAddCommGroup, TannakaDuality.FiniteGroup.equivHom_injective, SheafOfModules.pushforwardPushforwardEquivalence_counit_app_val_app, ModuleCat.extendScalars_μ, groupHomology.H0π_comp_H0Iso_hom_apply, ModuleCat.freeDesc_apply, CategoryTheory.ShortComplex.ShortExact.moduleCat_surjective_g, groupHomology.mapShortComplexH2_τ₃, FDRep.hom_action_ρ, ModuleCat.MonoidalCategory.tensorUnit_isAddCommGroup, PresheafOfModules.evaluation_map, CategoryTheory.linearCoyoneda_obj_obj_isModule, FDRep.dualTensorIsoLinHom_hom_hom, ModuleCat.homEquiv_extendScalarsId, ModuleCat.ExtendScalars.hom_ext_iff, groupHomology.d₂₁_comp_d₁₀_assoc, groupCohomology.coe_mapCocycles₂, groupCohomology.eq_d₀₁_comp_inv_assoc, groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc, ModuleCat.toKernelSubobject_arrow, groupCohomology.functor_map, CompHausLike.LocallyConstantModule.functorToPresheaves_obj_obj_isAddCommGroup, CategoryTheory.Iso.toLinearMap_toLinearEquiv, ModuleCat.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, ModuleCat.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, ModuleCat.restrictScalarsId'App_inv_apply, groupCohomology.mapShortComplexH1_τ₁, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, ModuleCat.smulShortComplex_exact, groupHomology.π_comp_H2Iso_inv_apply, PresheafOfModules.evaluation_preservesColimit, CoalgCat.toComon_obj, Rep.instAdditiveModuleCatCoinvariantsFunctor, PresheafOfModules.forgetToPresheafModuleCat_map, ModuleCat.MonModuleEquivalenceAlgebra.inverseObj_one, ModuleCat.localizedModule_hasInjectiveDimensionLE, groupCohomology.cochainsFunctor_obj, ModuleCat.restrictScalarsComp'App_inv_apply, FDRep.endRingEquiv_comp_ρ, CategoryTheory.ShortComplex.instPreservesHomologyModuleCatAbForget₂LinearMapIdCarrierAddMonoidHomCarrier, ModuleCat.isZero_of_subsingleton, ModuleCat.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, ModuleCat.instHasCoequalizers, ModuleCat.exteriorPower.functor_obj, TannakaDuality.FiniteGroup.equivHom_apply, ModuleCat.ihom_ev_app, groupCohomology.cocycles₁.d₁₂_apply, FDRep.simple_iff_char_is_norm_one, groupHomology.isoCycles₂_hom_comp_i_assoc, ModuleCat.FilteredColimits.colimit_add_mk_eq, groupHomology.comp_d₃₂_eq, groupCohomology.π_comp_H2Iso_hom, ModuleCat.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, ModuleCat.enoughInjectives, FGModuleCat.instIsMonoidalModuleCatIsFG, ModuleCat.extendScalars_assoc, groupCohomology.isIso_δ_of_isZero, ModuleCat.MonoidalCategory.associator_inv_apply, ModuleCat.preservesColimit_restrictScalars, groupCohomology.isoCocycles₂_inv_comp_iCocycles_assoc, ModuleCat.isSeparator, ModuleCat.instHasFiniteBiproducts, ModuleCat.exteriorPower.functor_map, groupHomology.δ₁_apply, instEnoughInjectivesModuleCatInt, Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIso_hom_f_hom_apply, groupHomology.H1π_eq_iff, ModuleCat.ExtendRestrictScalarsAdj.unit_app, ModuleCat.biprodIsoProd_inv_comp_fst_apply, groupHomology.d₃₂_comp_d₂₁_apply, FDRep.finrank_hom_simple_simple, FGModuleCat.instIsIsoCoimageImageComparison, ModuleCat.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, ModuleCat.forget₂_map, AlgebraicGeometry.tilde.toOpen_map_app, groupCohomology.d₀₁_eq_zero, ChainComplex.linearYonedaObj_X, ModuleCat.toMatrixModCat_obj_isModule

---

← Back to Index