zero 📖 | CompOp | 803 mathmath: CategoryTheory.ShortComplex.toCycles_comp_homologyπ, CategoryTheory.ShortComplex.toCycles_comp_homologyπ_assoc, CategoryTheory.Limits.eq_zero_of_mono_cokernel, CategoryTheory.Limits.zero_of_from_zero, CategoryTheory.ShortComplex.Homotopy.h₀_f_assoc, CategoryTheory.Limits.cokernelBiproductιIso_hom, TopModuleCat.hom_zero, HomologicalComplex.singleMapHomologicalComplex_hom_app_ne, CategoryTheory.ObjectProperty.isoModSerre_zero_iff, CategoryTheory.Limits.Bicone.π_of_isColimit, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app', CategoryTheory.Limits.inr_of_isLimit, CategoryTheory.Limits.coprod.inl_snd, CategoryTheory.ShortComplex.Homotopy.refl_h₀, HomologicalComplex.dFrom_comp_xNextIsoSelf, CategoryTheory.Preadditive.IsIso.comp_left_eq_zero, CategoryTheory.ShortComplex.hasHomology_of_zeros, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id_assoc, CategoryTheory.ShortComplex.RightHomologyData.ι_g', CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assoc, HomologicalComplex.double_d_eq_zero₀, CategoryTheory.ComposableArrows.IsComplex.zero'_assoc, CategoryTheory.Preadditive.commGrpEquivalence_functor_obj_grp_one, CategoryTheory.Abelian.LeftResolution.karoubi.F_obj_p, AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc, HomologicalComplex.dFrom_eq_zero, AlgebraicTopology.NormalizedMooreComplex.obj_d, CategoryTheory.BicartesianSq.of_is_biproduct₁, CategoryTheory.NonPreadditiveAbelian.diag_σ, CategoryTheory.Limits.monoFactorisationZero_I, CategoryTheory.Limits.biprod.inl_snd_assoc, CategoryTheory.IsPushout.of_is_bilimit', CategoryTheory.ShortComplex.homologyMap_zero, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hg', CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃_assoc, CategoryTheory.Abelian.Pseudoelement.pseudoZero_def, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π_assoc, TopModuleCat.hom_zero_apply, HomologicalComplex.extend.d_comp_eq_zero_iff, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hg, CategoryTheory.Limits.kernelBiprodSndIso_hom, CochainComplex.mappingCone.inr_f_fst_v, CategoryTheory.ShortComplex.zero_assoc, CategoryTheory.ShortComplex.RightHomologyData.wp, CategoryTheory.ShiftedHom.mk₀_zero, HomologicalComplex.homotopyCofiber.inrX_fstX_assoc, CategoryTheory.ShortComplex.RightHomologyData.wp_assoc, CategoryTheory.Limits.biproduct.ι_π_assoc, CategoryTheory.ShortComplex.exact_iff_iCycles_pOpcycles_zero, CategoryTheory.Abelian.LeftResolution.chainComplexMap_zero, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inl, CategoryTheory.ShortComplex.exact_iff_kernel_ι_comp_cokernel_π_zero, CategoryTheory.Functor.PreservesHomology.preservesKernels, HomologicalComplex.dTo_eq_zero, DerivedCategory.HomologySequence.comp_δ, CategoryTheory.ShortComplex.HasLeftHomology.of_zeros, CategoryTheory.DifferentialObject.d_squared_apply, CategoryTheory.Functor.homologySequence_comp_assoc, CategoryTheory.Subobject.factorThru_eq_zero, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂, CategoryTheory.Limits.prod.inl_snd, CategoryTheory.Limits.KernelFork.condition_assoc, CategoryTheory.Limits.zero_of_source_iso_zero, CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_inv, CategoryTheory.ShortComplex.LeftHomologyData.f'_π_assoc, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι_assoc, HomologicalComplex.biprod_inl_snd_f_assoc, Homotopy.nullHomotopicMap_f_eq_zero, AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_succ, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ_assoc, CategoryTheory.Abelian.LeftResolution.karoubi.F'_map_f, CategoryTheory.Preadditive.isColimitCoforkOfCokernelCofork_desc, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct, CategoryTheory.Limits.prod.inr_fst_assoc, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles_assoc, CategoryTheory.Limits.biprod.inlCokernelCofork_π, HomologicalComplex₂.d_f_comp_d_f, CategoryTheory.Limits.kernelForkBiproductToSubtype_cone, CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono, AlgebraicGeometry.Scheme.Modules.Hom.zero_app, HomologicalComplex₂.d₁_eq_zero', HomologicalComplex₂.D₁_D₁_assoc, CategoryTheory.Functor.homologySequence_comp, CategoryTheory.InjectiveResolution.of_def, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁, CategoryTheory.GradedObject.zero_apply, CategoryTheory.IsPushout.zero_top, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_isColimit, CategoryTheory.ShortComplex.homologyMap'_zero, CategoryTheory.Preadditive.IsIso.comp_right_eq_zero, CategoryTheory.Limits.Sigma.ι_π_assoc, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_mono₂, CategoryTheory.Limits.kernel.condition_apply, CategoryTheory.Limits.equalizer_as_kernel, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃_assoc, HomologicalComplex.extend.d_none_eq_zero', CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃, HomologicalComplex₂.D₁_D₁, CategoryTheory.zero_map, CategoryTheory.InjectiveResolution.complex_d_comp, CategoryTheory.Limits.PreservesCokernel.of_iso_comparison, HomologicalComplex.single_obj_d, CategoryTheory.ShortComplex.ShortExact.comp_δ, CategoryTheory.Limits.kernelBiprodFstIso_hom, CategoryTheory.Limits.monoFactorisationZero_e, CategoryTheory.IsPullback.inr_fst, HomologicalComplex₂.D₂_D₂, CategoryTheory.ShortComplex.Homotopy.g_h₃_assoc, HomologicalComplex.d_toCycles_assoc, CategoryTheory.kernel_zero_of_nonzero_from_simple, HomologicalComplex.xPrevIsoSelf_comp_dTo, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂, CategoryTheory.Limits.isoZeroOfEpiZero_hom, CategoryTheory.Limits.kernelBiproductπIso_hom, CategoryTheory.Abelian.tfae_epi, HomologicalComplex.d_comp_d_assoc, CategoryTheory.Limits.BinaryBicone.sndKernelFork_ι, CochainComplex.fromSingle₀Equiv_apply_coe, HomologicalComplex.dgoToHomologicalComplex_obj_d, CategoryTheory.Localization.liftNatTrans_zero, HomotopyCategory.quotient_map_eq_zero_iff, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero', CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.f', Homotopy.nullHomotopicMap'_f_eq_zero, HomologicalComplex₂.d₂_eq_zero, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hf', CategoryTheory.Biprod.unipotentLower_inv, CategoryTheory.ShortComplex.Splitting.rightHomologyData_ι, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inl, CategoryTheory.ShortComplex.hasHomology_of_hasCokernel, CategoryTheory.Idempotents.Karoubi.hom_eq_zero_iff, CategoryTheory.Limits.biprod.inr_fst, CategoryTheory.kernelCokernelCompSequence.ι_φ, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_inv, CategoryTheory.Preadditive.isSeparator_iff, HomologicalComplex.fromOpcycles_d_assoc, CategoryTheory.IsPullback.zero_top, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₃_assoc, CategoryTheory.ShortComplex.Homotopy.refl_h₃, CochainComplex.HomComplex.Cochain.single_zero, CategoryTheory.ShortComplex.SnakeInput.δ_L₃_f, CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff, CategoryTheory.Limits.coker.condition_assoc, CategoryTheory.Limits.BinaryBicone.inl_snd_assoc, CategoryTheory.Preadditive.isSeparating_iff, CategoryTheory.Abelian.FunctorCategory.coimageImageComparison_app, CategoryTheory.ShortComplex.iCycles_g, DerivedCategory.HomologySequence.mono_homologyMap_mor₁_iff, HomologicalComplex.truncGE'.d_comp_d, CategoryTheory.Limits.cokernel.π_zero_isIso, CategoryTheory.Endofunctor.coalgebraPreadditive_homGroup_zero_f, HomologicalComplex.extend.d_none_eq_zero, HomologicalComplex.mapBifunctor₂₃.ιOrZero_eq_zero, CochainComplex.ConnectData.d_comp_d, HomologicalComplex.d_pOpcycles, CategoryTheory.Limits.isIsoZero_iff_source_target_isZero, CategoryTheory.Limits.Pi.ι_π_of_ne, CategoryTheory.ShiftedHom.zero_comp, CategoryTheory.ShortComplex.Homotopy.refl_h₂, HomologicalComplex.fromOpcycles_eq_zero, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f_assoc, ChainComplex.toSingle₀Equiv_apply_coe, HomologicalComplex.homologyι_opcyclesToCycles_assoc, CategoryTheory.NormalEpi.w, CategoryTheory.Limits.coequalizer_as_cokernel, CategoryTheory.Limits.HasZeroObject.zeroIsoTerminal_hom, CategoryTheory.IsPushout.inl_snd', CategoryTheory.ShortComplex.π₁Toπ₂_comp_π₂Toπ₃, CategoryTheory.Limits.Pi.ι_π, CategoryTheory.BicartesianSq.of_has_biproduct₂, HomologicalComplex₂.d_f_comp_d_f_assoc, HomologicalComplex.homotopyCofiber.inlX_sndX_assoc, HomologicalComplex.homologyι_comp_fromOpcycles, CochainComplex.HomComplex.Cochain.toSingleMk_v_eq_zero, CategoryTheory.Limits.zero_of_target_iso_zero', CategoryTheory.Limits.biprod.fstKernelFork_ι, AlgebraicTopology.DoldKan.QInfty_f_0, CategoryTheory.ShortComplex.RightHomologyData.wι_assoc, CategoryTheory.InjectiveResolution.ι_f_succ, CategoryTheory.Limits.comp_zero, CategoryTheory.Limits.monoFactorisationZero_m, CategoryTheory.Limits.preservesKernel_zero, CategoryTheory.Functor.map_zero, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero_assoc, AlgebraicTopology.AlternatingFaceMapComplex.d_squared, CategoryTheory.Limits.inr_pushoutZeroZeroIso_hom, HomologicalComplex.mapBifunctorMapHomotopy.zero₁, CategoryTheory.Preadditive.epi_iff_cancel_zero, Homotopy.dNext_zero_chainComplex, HomologicalComplex.mapBifunctor₂₃.d₃_eq_zero, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d_assoc, DerivedCategory.to_singleFunctor_obj_eq_zero_of_injective, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eq, CategoryTheory.Limits.kernelBiprodFstIso_inv, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_mono₃, CategoryTheory.Limits.kernelBiproductToSubtypeIso_hom, CategoryTheory.Limits.CokernelCofork.condition, CochainComplex.HomComplex.Cochain.zero_v, CategoryTheory.Limits.cokernel.condition, CategoryTheory.NonPreadditiveAbelian.sub_zero, CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.g, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inr, CategoryTheory.IsPushout.zero_bot, CategoryTheory.Limits.BinaryBicone.ofLimitCone_inr, CategoryTheory.Abelian.LeftResolution.karoubi.F_map_f, CategoryTheory.IsPushout.zero_left, HomologicalComplex.mapBifunctor₁₂.d₂_eq_zero, CategoryTheory.Biprod.unipotentUpper_hom, CategoryTheory.ShortComplex.Homotopy.ofEq_h₂, CategoryTheory.Subobject.bot_factors_iff_zero, CategoryTheory.MonoidalPreadditive.whiskerLeft_zero, HomologicalComplex.iCycles_d, HomologicalComplex.mapBifunctor₁₂.ιOrZero_eq_zero, CategoryTheory.Limits.pullbackZeroZeroIso_inv_fst, CategoryTheory.InjectiveResolution.extMk_zero, ChainComplex.mk_congr_succ_X₃, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₂_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_hom_snd, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles_assoc, HomologicalComplex.dTo_comp_dFrom, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f, HomologicalComplex₂.D₁_shape, CategoryTheory.ComposableArrows.IsComplex.mono_cokerToKer', CategoryTheory.Limits.cokernelBiprodInlIso_inv, CategoryTheory.DifferentialObject.d_squared, CategoryTheory.ComposableArrows.IsComplex.zero_assoc, CategoryTheory.ObjectProperty.monoModSerre_zero_iff, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φH, CategoryTheory.Limits.image.ι_zero, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext, CategoryTheory.Limits.kernel.ι_of_mono, CategoryTheory.Limits.inl_of_isLimit, CategoryTheory.Pretriangulated.contractibleTriangle_mor₂, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zero, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.hf, CategoryTheory.Abelian.LeftResolution.karoubi.F'_obj_p, CategoryTheory.ShortComplex.Homotopy.ofEq_h₀, HomologicalComplex.opcyclesToCycles_homologyπ, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_inv, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_of_epi₁, CategoryTheory.Limits.biprod.sndKernelFork_ι, CategoryTheory.Preadditive.forkOfKernelFork_pt, CochainComplex.HomComplex.Cocycle.toSingleMk_zero, AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero, CategoryTheory.Limits.ker.condition, HomologicalComplex.homotopyCofiber.inrX_fstX, CategoryTheory.Limits.BinaryBicone.inr_fst_assoc, DerivedCategory.HomologySequence.comp_δ_assoc, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁, CategoryTheory.Functor.map_eq_zero_iff, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₁_iff, SimplicialObject.Splitting.cofan_inj_comp_PInfty_eq_zero, SimplicialObject.Splitting.ιSummand_comp_d_comp_πSummand_eq_zero, CategoryTheory.Biprod.unipotentLower_hom, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_K, CategoryTheory.Limits.zero_of_to_zero, CategoryTheory.Limits.snd_of_isColimit, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_epi₂, HomologicalComplex.d_toCycles, CategoryTheory.Limits.id_zero, CategoryTheory.Limits.cokernelBiprodInrIso_inv, CategoryTheory.IsPushout.inr_fst, CategoryTheory.Pretriangulated.contractible_distinguished₂, CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundary, CategoryTheory.Functor.homologySequenceδ_comp_assoc, HomologicalComplex.d_pOpcycles_assoc, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_leftAdd, CategoryTheory.IsPullback.inl_snd, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁_assoc, CategoryTheory.ProjectiveResolution.of_def, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₁_iff, Homotopy.zero, CategoryTheory.Limits.imageSubobject_zero_arrow, CategoryTheory.ProjectiveResolution.π_f_succ, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles_assoc, CategoryTheory.IsPushout.of_hasBinaryCoproduct, CategoryTheory.Idempotents.zero_def, CategoryTheory.IsPullback.of_hasBinaryProduct, CategoryTheory.Limits.imageSubobject_zero, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_inv, CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary, HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary, Homotopy.extend.hom_eq_zero₁, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id, PresheafOfModules.toFreeYonedaCoproduct_fromFreeYonedaCoproduct_assoc, AlgebraicTopology.AlternatingCofaceMapComplex.d_squared, CategoryTheory.Limits.cokernel.π_of_zero, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_pt, CategoryTheory.Triangulated.TStructure.zero, HomologicalComplex.extend_single_d, CategoryTheory.projective_iff_llp_epimorphisms_zero, CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary_assoc, HomologicalComplex.mapBifunctor.d₁_eq_zero, HomologicalComplex₂.d₁_eq_zero, CategoryTheory.ObjectProperty.epiModSerre_zero_iff, CochainComplex.singleFunctor_obj_d, CategoryTheory.ShortComplex.LeftHomologyData.f'_π, CategoryTheory.Limits.CokernelCofork.mapIsoOfIsColimit_hom, CategoryTheory.Subobject.mk_eq_bot_iff_zero, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_hom, HomologicalComplex.extend_d_to_eq_zero, CategoryTheory.Functor.mapZeroObject_inv, AlgebraicTopology.DoldKan.HigherFacesVanish.comp_δ_eq_zero, CategoryTheory.Limits.coker.condition, CategoryTheory.ShiftedHom.comp_zero, CategoryTheory.NatTrans.app_zero, CategoryTheory.ShortComplex.Homotopy.refl_h₁, CategoryTheory.ShortComplex.Exact.shortExact, CategoryTheory.Limits.KernelFork.condition, CategoryTheory.Limits.biproduct.fromSubtype_π, CategoryTheory.Limits.kernel.ι_of_zero, prevD_eq_zero, CategoryTheory.ShortComplex.exact_and_epi_g_iff_g_is_cokernel, CategoryTheory.Mat_.isoBiproductEmbedding_hom, CategoryTheory.NonPreadditiveAbelian.add_zero, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂, DerivedCategory.HomologySequence.epi_homologyMap_mor₁_iff, CategoryTheory.InjectiveResolution.ι_f_zero_comp_complex_d, CategoryTheory.Functor.PreservesHomology.preservesCokernels, CategoryTheory.ShortComplex.HasLeftHomology.of_hasCokernel, CategoryTheory.Preadditive.cokernelCoforkOfCofork_π, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype, CategoryTheory.Functor.comp_homologySequenceδ, DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff, CategoryTheory.Limits.cokernelBiprodInrIso_hom, CategoryTheory.Limits.kernel.condition, CategoryTheory.MonoOver.bot_arrow_eq_zero, CategoryTheory.ShortComplex.LeftHomologyData.wπ_assoc, CategoryTheory.Biprod.column_nonzero_of_iso, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.g', CochainComplex.HomComplex.Cochain.fromSingleMk_zero, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_pt, CategoryTheory.Limits.biprod.inl_snd, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_Q, CochainComplex.mappingCone.inl_v_snd_v_assoc, HomologicalComplex.cylinder.inlX_π, CategoryTheory.Limits.Sigma.ι_π, HomologicalComplex.extend.rightHomologyData.d_comp_desc_eq_zero_iff, HomologicalComplex.biprod_inr_fst_f, CategoryTheory.Limits.cokernel.condition_assoc, TopModuleCat.comp_cokerπ, CategoryTheory.Limits.kernelSubobject_arrow_comp_apply, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_hom_inv_id, CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d, CochainComplex.mappingCone.inr_f_triangle_mor₃_f, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_snd, AlgebraicTopology.DoldKan.Hσ_eq_zero, CochainComplex.ConnectData.d₀_comp, HomologicalComplex.tensor_unit_d₂, CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary_assoc, ChainComplex.mk'_congr_succ'_d, CategoryTheory.Limits.cokernelBiproductιIso_inv, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_fst, CategoryTheory.Limits.kernelBiproductπIso_inv, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₁, HomologicalComplex.homologyι_comp_fromOpcycles_assoc, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_hom, CategoryTheory.Preadditive.kernelForkOfFork_ι, CategoryTheory.Pretriangulated.Triangle.zero_hom₁, HomologicalComplex.cylinder.inlX_π_assoc, CategoryTheory.ShortComplex.SnakeInput.L₀_g_δ, HomologicalComplex₂.d₂_eq_zero', CategoryTheory.ShortComplex.Splitting.leftHomologyData_π, CategoryTheory.Limits.prod.inl_snd_assoc, HomologicalComplex.d_comp_d', CategoryTheory.Limits.bicone_ι_π_ne_assoc, imageToKernel_epi_of_zero_of_mono, zero_comp, HomologicalComplex.zero_f, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃, HomologicalComplex.homotopyCofiber.inrCompHomotopy_hom_eq_zero, CategoryTheory.ShortComplex.cyclesMap'_zero, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_epi₁, CategoryTheory.ShortComplex.zero_τ₃, CategoryTheory.ShortComplex.HasRightHomology.of_hasCokernel, CategoryTheory.Limits.biproduct.ι_π_ne, CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₃, CategoryTheory.Limits.biproduct.fromSubtype_π_assoc, CategoryTheory.ShortComplex.kernel_ι_comp_cokernel_π_comp_cokernelToAbelianCoimage, AlgebraicTopology.DoldKan.Q_f_0_eq, CategoryTheory.Triangulated.TStructure.zero_of_isLE_of_isGE, CategoryTheory.ShortComplex.RightHomologyData.wι, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero, CategoryTheory.IsPullback.zero_left, CategoryTheory.ShortComplex.iCycles_g_assoc, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₁_assoc, CategoryTheory.ShortComplex.Exact.mono_g_iff, CategoryTheory.ShortComplex.rightHomologyMap_zero, CategoryTheory.ShortComplex.exact_iff_i_p_zero, CategoryTheory.Limits.Bicone.ofLimitCone_ι, CategoryTheory.Abelian.Pseudoelement.zero_morphism_ext', Homotopy.ofEq_hom, HomologicalComplex₂.D₂_shape, CategoryTheory.Preadditive.mono_iff_isZero_kernel', CategoryTheory.ShortComplex.LeftHomologyData.wi, Action.zero_hom, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_inl, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_π, CategoryTheory.Preadditive.isCoseparating_iff, CategoryTheory.MonoidalPreadditive.tensor_zero, CategoryTheory.Adjunction.homAddEquiv_symm_zero, CategoryTheory.IsPushout.of_isBilimit, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero, HomologicalComplex.homotopyCofiber.inlX_sndX, HomologicalComplex.truncGE'.d_comp_d_assoc, CategoryTheory.ShortComplex.cyclesMap_zero, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φH, AddCommGrpCat.kernelIsoKer_inv_comp_ι, CategoryTheory.ShortComplex.HasRightHomology.of_hasKernel, HomologicalComplex.ιMapBifunctorOrZero_eq_zero, CategoryTheory.Pretriangulated.binaryProductTriangle_mor₃, CategoryTheory.Limits.biproduct.fromSubtype_eq_lift, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty_assoc, CategoryTheory.Limits.eq_zero_of_epi_kernel, CategoryTheory.Limits.IsZero.map, CategoryTheory.ComposableArrows.isComplex₂_iff, SheafOfModules.Presentation.map_relations_I, CategoryTheory.Functor.shiftMap_zero, CategoryTheory.ShortComplex.toCycles_comp_leftHomologyπ, AlgebraicTopology.NormalizedMooreComplex.d_squared, CategoryTheory.Limits.kernelSubobject_factors_iff, CategoryTheory.ProjectiveResolution.complex_d_succ_comp, CategoryTheory.Abelian.Ext.zero_hom, HomologicalComplex.homotopyCofiber.shape, Homotopy.mkCoinductiveAux₂_zero, CategoryTheory.ComposableArrows.Exact.cokerIsoKer'_inv_hom_id_assoc, CategoryTheory.ShortComplex.LeftHomologyData.wπ, CategoryTheory.Abelian.Ext.mk₀_zero, SheafOfModules.Presentation.mapRelations_mapGenerators, CategoryTheory.IsPushout.inr_fst', CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₂₃_assoc, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero_assoc, CategoryTheory.Limits.KernelFork.app_one, CategoryTheory.ShortComplex.RightHomologyData.ι_g'_assoc, CategoryTheory.Functor.whiskerRight_zero, CategoryTheory.Limits.kernel.ι_zero_isIso, CategoryTheory.NonPreadditiveAbelian.neg_add_cancel, CategoryTheory.Limits.isKernelCompMono_lift, CategoryTheory.ShortComplex.LeftHomologyMapData.zero_φK, CategoryTheory.Preadditive.coforkOfCokernelCofork_π, CategoryTheory.ShortComplex.SnakeInput.L₀X₂ToP_comp_φ₁_assoc, CategoryTheory.Limits.biprod.inrCokernelCofork_π, CategoryTheory.Limits.Pi.ι_π_assoc, CategoryTheory.Limits.isoZeroOfMonoZero_inv, CategoryTheory.ShortComplex.ShortExact.δ_comp_assoc, CochainComplex.HomComplex.Cocycle.fromSingleMk_zero, HomologicalComplex.zero_f_apply, CategoryTheory.ProjectiveResolution.extMk_zero, HomologicalComplex.toCycles_eq_zero, CategoryTheory.Monad.algebraPreadditive_homGroup_zero_f, CochainComplex.mappingCone.inr_f_fst_v_assoc, CategoryTheory.IsPullback.of_hasBinaryBiproduct, CategoryTheory.IsPushout.inl_snd, CategoryTheory.Limits.CokernelCofork.π_mapOfIsColimit_assoc, CategoryTheory.IsPullback.of_is_bilimit', ChainComplex.mk'_d, HomologicalComplex.singleMapHomologicalComplex_inv_app_ne, CategoryTheory.ShortComplex.HasLeftHomology.of_hasKernel, HomologicalComplex.dgoToHomologicalComplex_map_f, CategoryTheory.Limits.BinaryBicone.inrCokernelCofork_π, CategoryTheory.Limits.pullbackZeroZeroIso_hom_fst, CategoryTheory.Limits.isIso_kernelSubobject_zero_arrow, CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy.f, HomologicalComplex.cyclesMap_zero, CategoryTheory.Limits.unop_zero, CategoryTheory.Pretriangulated.binaryBiproductTriangle_mor₃, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_inv, HomologicalComplex.homologyMap_zero, CategoryTheory.ShortComplex.opcyclesMap_zero, CategoryTheory.Subobject.bot_arrow, CategoryTheory.Limits.IsZero.iff_isSplitEpi_eq_zero, CategoryTheory.ShortComplex.HomologyData.exact_iff_i_p_zero, HomologicalComplex.toCycles_comp_homologyπ, CochainComplex.ConnectData.d_comp_d_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_snd, HomologicalComplex₂.D₂_D₂_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₂_iff, CategoryTheory.IsPullback.inl_snd', CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₂_assoc, HomologicalComplex.xPrevIsoSelf_comp_dTo_assoc, CategoryTheory.HomOrthogonal.matrixDecompositionAddEquiv_symm_apply, HomologicalComplex.mapBifunctor₁₂.d₃_eq_zero, CategoryTheory.ShortComplex.RightHomologyMapData.zero_φQ, CochainComplex.toSingle₀Equiv_symm_apply_f_succ, CategoryTheory.Limits.zero_of_source_iso_zero', CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc, CategoryTheory.Limits.IsZero.eq_zero_of_tgt, CategoryTheory.Adjunction.homAddEquiv_zero, DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_epi₂, CategoryTheory.Biprod.unipotentUpper_inv, CategoryTheory.IsPullback.of_has_biproduct, AlgebraicTopology.DoldKan.Γ₀.Obj.Termwise.mapMono_eq_zero, CategoryTheory.IsGrothendieckAbelian.GabrielPopescuAux.kernel_ι_d_comp_d, CategoryTheory.Limits.PreservesKernel.of_iso_comparison, CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι_assoc, HomologicalComplex.extend_d_from_eq_zero, CategoryTheory.NonPreadditiveAbelian.lift_map_assoc, CategoryTheory.Subobject.bot_eq_zero, Homotopy.extend.hom_eq_zero₂, CategoryTheory.ShortComplex.zero, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_ι, CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary, HomologicalComplex.toCycles_comp_homologyπ_assoc, CategoryTheory.ShortComplex.exact_and_mono_f_iff_f_is_kernel, CategoryTheory.Limits.CokernelCofork.condition_assoc, AlgebraicTopology.DoldKan.hσ'_eq_zero, CategoryTheory.NormalMono.w, HomologicalComplex₂.shape_f, CategoryTheory.Pretriangulated.Triangle.zero_hom₃, CategoryTheory.MonoidalPreadditive.zero_tensor, CategoryTheory.Limits.fst_of_isColimit, CategoryTheory.IsGrothendieckAbelian.instInjectiveZMonomorphismsRlpMonoMapFactorizationDataRlpOfNatHom, CategoryTheory.Limits.coprod.inr_fst_assoc, CategoryTheory.Limits.inr_pushoutZeroZeroIso_inv, CategoryTheory.Limits.Bicone.ι_π, CategoryTheory.Limits.biprod.inr_fst_assoc, CategoryTheory.ShortComplex.rightHomologyι_descOpcycles_π_eq_zero_of_boundary_assoc, HomologicalComplex.extend.comp_d_eq_zero_iff, CategoryTheory.Abelian.Pseudoelement.zero_eq_zero, CategoryTheory.shift_zero_eq_zero, CategoryTheory.Limits.BinaryBicone.inlCokernelCofork_π, CategoryTheory.IsPullback.zero_bot, CategoryTheory.Limits.Sigma.ι_π_of_ne_assoc, CategoryTheory.Limits.CokernelCofork.map_condition, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₃₁_assoc, SheafOfModules.Presentation.mapRelations_mapGenerators_assoc, CategoryTheory.ShortComplex.homologyι_comp_fromOpcycles, CategoryTheory.epi_from_simple_zero_of_not_iso, CategoryTheory.Abelian.coimage.comp_π_eq_zero, CategoryTheory.Limits.zero_of_target_iso_zero, CochainComplex.ConnectData.shape, CategoryTheory.Triangulated.TStructure.zero', CategoryTheory.IsPullback.zero_right, AlgebraicTopology.DoldKan.σ_comp_PInfty, CochainComplex.HomComplex.Cochain.toSingleMk_zero, CategoryTheory.Abelian.Pseudoelement.pseudoZero_aux, CategoryTheory.Limits.kernelZeroIsoSource_hom, CategoryTheory.Pretriangulated.contractibleTriangle_mor₃, CategoryTheory.ShortComplex.ShortExact.δ_comp, CategoryTheory.Preadditive.isLimitForkOfKernelFork_lift, CategoryTheory.Preadditive.epi_iff_isZero_cokernel', CategoryTheory.Limits.CokernelCofork.map_π, CategoryTheory.ShortComplex.homologyι_descOpcycles_eq_zero_of_boundary_assoc, HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary_assoc, Homotopy.prevD_zero_cochainComplex, CategoryTheory.Limits.MonoFactorisation.kernel_ι_comp, CategoryTheory.HomOrthogonal.eq_zero, CategoryTheory.Mat_.isoBiproductEmbedding_inv, CategoryTheory.Limits.biproduct.toSubtype_eq_desc, CategoryTheory.Abelian.Ext.mk₀_eq_zero_iff, CategoryTheory.Limits.Bicone.ofColimitCocone_π, CategoryTheory.kernelCokernelCompSequence.φ_π, CochainComplex.ConnectData.d₀_comp_assoc, CategoryTheory.Limits.isoZeroOfEpiZero_inv, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_inv, CategoryTheory.Limits.kernel.condition_assoc, CategoryTheory.Limits.cokernelBiprodInlIso_hom, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles, CategoryTheory.Limits.biproduct.ι_π, HomologicalComplex.d_comp_d, ChainComplex.mk_congr_succ_d₂, CategoryTheory.Abelian.image.ι_comp_eq_zero, CategoryTheory.IsPushout.of_hasBinaryBiproduct, HomologicalComplex.mapBifunctor.d₂_eq_zero, CategoryTheory.ShortComplex.Splitting.s_r, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_fst, ChainComplex.chainComplex_d_succ_succ_zero, CategoryTheory.Limits.Pi.ι_π_of_ne_assoc, CategoryTheory.ShortComplex.abelianImageToKernel_comp_kernel_ι_comp_cokernel_π, CategoryTheory.ComposableArrows.IsComplex.epi_cokerToKer', CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_epi₃, AlgebraicTopology.DoldKan.N₂_obj_X_d, CategoryTheory.BicartesianSq.of_is_biproduct₂, CategoryTheory.Triangulated.instNonemptyOctahedron, SimplicialObject.Splitting.cofan_inj_πSummand_eq_zero_assoc, CategoryTheory.Limits.pullbackZeroZeroIso_inv_snd, CategoryTheory.Limits.KernelFork.mapIsoOfIsLimit_hom, CategoryTheory.BicartesianSq.of_has_biproduct₁, CategoryTheory.Endofunctor.algebraPreadditive_homGroup_zero_f, CategoryTheory.Limits.kernelZeroIsoSource_inv, CochainComplex.cm5b.I_d, CategoryTheory.ShortComplex.Homotopy.ofEq_h₁, CategoryTheory.IsPullback.of_isBilimit, CategoryTheory.ComposableArrows.Exact.isIso_cokerToKer', CategoryTheory.Limits.HasZeroObject.zeroIsoIsInitial_hom, CategoryTheory.Limits.kernelBiprodSndIso_inv, CategoryTheory.Limits.inl_pushoutZeroZeroIso_inv, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_iff_mono₂, AlgebraicGeometry.tilde.map_zero, CochainComplex.ConnectData.comp_d₀, SimplicialObject.Splitting.comp_PInfty_eq_zero_iff, CategoryTheory.Limits.BinaryBicone.ofColimitCocone_snd, CategoryTheory.MonoidalPreadditive.zero_whiskerRight, CategoryTheory.Abelian.FunctorCategory.imageObjIso_hom, CategoryTheory.Limits.KernelFork.map_condition, HomologicalComplex.opcyclesToCycles_homologyπ_assoc, CochainComplex.mappingCone.inl_v_descShortComplex_f, CategoryTheory.Limits.Sigma.ι_π_of_ne, AddCommGrpCat.kernelIsoKer_hom_comp_subtype, AlgebraicTopology.DoldKan.degeneracy_comp_PInfty, HomologicalComplex.mapBifunctor₁₂.d₁_eq_zero, CategoryTheory.Limits.kernelSubobject_arrow_comp_assoc, CategoryTheory.IsPushout.zero_right, CategoryTheory.Limits.ker.condition_assoc, CategoryTheory.Localization.Preadditive.add'_zero, CategoryTheory.Limits.coprod.inr_fst, HomologicalComplex.mapBifunctor.d₂_eq_zero', CategoryTheory.Limits.zero_app, CategoryTheory.Limits.isoZeroOfMonoZero_hom, CategoryTheory.Limits.BinaryBicone.fstKernelFork_ι, SimplicialObject.Splitting.σ_comp_πSummand_id_eq_zero, CochainComplex.HomComplex.Cochain.single_v_eq_zero', HomologicalComplex.homologyι_opcyclesToCycles, CategoryTheory.Pretriangulated.Triangle.mor₁_eq_zero_of_epi₃, CategoryTheory.Preadditive.forkOfKernelFork_ι, CategoryTheory.Mat_.id_apply, CochainComplex.mappingCone.inr_f_triangle_mor₃_f_assoc, CochainComplex.cochainComplex_d_succ_succ_zero, CategoryTheory.Abelian.tfae_mono, CategoryTheory.ShortComplex.Homotopy.g_h₃, CategoryTheory.IsPushout.of_has_biproduct, CategoryTheory.Preadditive.isCoseparator_iff, CategoryTheory.Limits.KernelFork.map_ι, CategoryTheory.Limits.zero_comp, CochainComplex.HomComplex.CohomologyClass.toHom_mk_eq_zero_iff, CategoryTheory.MonoOver.initialTo_b_eq_zero, CategoryTheory.Pretriangulated.Triangle.isZero₃_iff, HomologicalComplex.mapBifunctor.d₁_eq_zero', CategoryTheory.ShortComplex.Homotopy.ofEq_h₃, CategoryTheory.NonPreadditiveAbelian.diag_σ_assoc, CategoryTheory.Limits.biproduct.ι_toSubtype, CochainComplex.mappingCone.inl_v_snd_v, CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary, HomologicalComplex.unit_tensor_d₁, CategoryTheory.Limits.IsZero.eq_zero_of_src, CategoryTheory.SemiadditiveOfBinaryBiproducts.isUnital_rightAdd, CategoryTheory.DifferentialObject.d_squared_assoc, CategoryTheory.Limits.biproduct.ι_toSubtype_assoc, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assoc, CategoryTheory.Abelian.FunctorCategory.functor_category_isIso_coimageImageComparison, CategoryTheory.Limits.HasZeroObject.zeroIsoIsTerminal_inv, CochainComplex.ConnectData.comp_d₀_assoc, AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_f, CategoryTheory.ShortComplex.HasRightHomology.of_zeros, CategoryTheory.Limits.IsZero.iff_id_eq_zero, CategoryTheory.ShortComplex.zero_τ₁, CategoryTheory.ShortComplex.Exact.rightHomologyDataOfIsColimitCokernelCofork_p, CategoryTheory.Limits.cokernel.π_of_epi, CategoryTheory.ShiftedHom.map_zero, CochainComplex.HomComplex.Cochain.fromSingleMk_v_eq_zero, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_of_mono₁, CategoryTheory.ShortComplex.exact_iff_of_forks, CategoryTheory.Functor.PreservesHomology.preservesCokernel, CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.f'_eq, HomologicalComplex.extend.leftHomologyData.lift_d_comp_eq_zero_iff, CategoryTheory.Limits.BinaryBicone.inl_snd, CategoryTheory.ShortComplex.liftCycles_homologyπ_eq_zero_of_boundary, CategoryTheory.HomOrthogonal.matrixDecomposition_symm_apply, CategoryTheory.NonPreadditiveAbelian.lift_map, HomologicalComplex.homologyι_descOpcycles_eq_zero_of_boundary, CategoryTheory.Limits.IsZero.iff_isSplitMono_eq_zero, HomologicalComplex.fromOpcycles_d, HomologicalComplex.iCycles_d_assoc, CategoryTheory.Limits.op_zero, CategoryTheory.ShortComplex.rightHomologyι_comp_fromOpcycles, SheafOfModules.Presentation.IsFinite.finite_relations, CategoryTheory.ShortComplex.SnakeInput.w₀₂_τ₃, CategoryTheory.ObjectProperty.rightOrthogonal_iff, CategoryTheory.Preadditive.one_def, CategoryTheory.Pretriangulated.Triangle.mor₂_eq_zero_iff_mono₃, CategoryTheory.Mat_.id_def, CategoryTheory.DifferentialObject.d_squared_apply_assoc, CategoryTheory.Limits.biproduct.toSubtype_fromSubtype_assoc, CochainComplex.HomComplex.Cochain.equivHomotopy_symm_apply_hom, CategoryTheory.Limits.CokernelCofork.map_condition_assoc, CategoryTheory.Limits.hasPullback_over_zero, HomologicalComplex.extendMap_f_eq_zero, CategoryTheory.ShortComplex.Exact.isZero_X₂_iff, AlgebraicTopology.DoldKan.σ_comp_P_eq_zero, CategoryTheory.NonPreadditiveAbelian.add_neg_cancel, CategoryTheory.Subobject.factors_zero, CategoryTheory.IsPullback.inr_fst', CategoryTheory.ShortComplex.LeftHomologyData.wi_assoc, CategoryTheory.Pretriangulated.Triangle.isZero₁_iff, HomologicalComplex₂.ιTotalOrZero_eq_zero, HomologicalComplex.double_d_eq_zero₁, CategoryTheory.ShortComplex.SnakeInput.w₁₃_τ₁, CategoryTheory.ShortComplex.Exact.epi_f_iff, HomologicalComplex.truncGE'.homologyι_truncGE'XIsoOpcycles_inv_d, CategoryTheory.Limits.CokernelCofork.π_eq_zero, CategoryTheory.Limits.bicone_ι_π_ne, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac_assoc, CategoryTheory.NonPreadditiveAbelian.lift_σ, CategoryTheory.Mat_.id_apply_of_ne, CategoryTheory.Limits.hasPushout_over_zero, CategoryTheory.NonPreadditiveAbelian.lift_σ_assoc, HomologicalComplex.opcyclesMap_zero, imageToKernel_epi_of_epi_of_zero, AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_f_assoc, CategoryTheory.Pretriangulated.Triangle.mor₃_eq_zero_iff_mono₁, CategoryTheory.Abelian.Pseudoelement.eq_zero_iff, HomologicalComplex.shortComplexTruncLE_shortExact_δ_eq_zero, CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.hf, CategoryTheory.Limits.BinaryBicone.inr_fst, CategoryTheory.Limits.cokernelZeroIsoTarget_hom, DerivedCategory.HomologySequence.δ_comp_assoc, CategoryTheory.Limits.CokernelCofork.IsColimit.isZero_of_epi, CategoryTheory.Limits.cokernelCoforkBiproductFromSubtype_cocone, DerivedCategory.HomologySequence.δ_comp, HomologicalComplex.biprod_inr_fst_f_assoc, CategoryTheory.Limits.kernelSubobject_arrow_comp, CategoryTheory.NonPreadditiveAbelian.neg_def, TopModuleCat.kerι_comp, CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork_i, CategoryTheory.Pretriangulated.comp_distTriang_mor_zero₁₂_assoc, HomologicalComplex.extend.mapX_none, CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero_assoc, CategoryTheory.Limits.biproduct.ι_π_ne_assoc, CategoryTheory.ShortComplex.leftHomologyMap_zero, CategoryTheory.Limits.cokernelZeroIsoTarget_inv, HomologicalComplex.shape, CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac, Homotopy.refl_hom, CochainComplex.HomComplex.Cochain.ofHoms_zero, CategoryTheory.ShortComplex.liftCycles_leftHomologyπ_eq_zero_of_boundary, CategoryTheory.Pretriangulated.contractible_distinguished₁, HomologicalComplex.mapBifunctor₂₃.d₁_eq_zero, DerivedCategory.HomologySequence.epi_homologyMap_mor₂_iff, CategoryTheory.Limits.coprod.inl_snd_assoc, CategoryTheory.Localization.Preadditive.zero_add', dNext_eq_zero, CategoryTheory.Abelian.FunctorCategory.coimageObjIso_hom, CategoryTheory.Localization.Preadditive.neg'_add'_self, CategoryTheory.ComposableArrows.IsComplex.zero, CategoryTheory.Limits.cokernelBiproductFromSubtypeIso_inv, CategoryTheory.ShortComplex.leftHomologyMap'_zero, CategoryTheory.Limits.prod.inr_fst, CategoryTheory.injective_iff_rlp_monomorphisms_zero, CategoryTheory.ShortComplex.rightHomologyMap'_zero, HomologicalComplex.biprod_inl_snd_f, CategoryTheory.Limits.preservesCokernel_zero, Homotopy.mkInductiveAux₂_zero, CategoryTheory.Functor.mapZeroObject_hom, ChainComplex.alternatingConst_map_f, CategoryTheory.Functor.homologySequenceδ_comp, ChainComplex.fromSingle₀Equiv_symm_apply_f_succ, CategoryTheory.Limits.kernelForkBiproductToSubtype_isLimit, CategoryTheory.Limits.hasImage_zero, CategoryTheory.Limits.kernelBiproductToSubtypeIso_inv, CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom, HomologicalComplex.dFrom_comp_xNextIsoSelf_assoc, comp_zero, CategoryTheory.NonPreadditiveAbelian.sub_self, CategoryTheory.ShortComplex.Homotopy.h₀_f, CategoryTheory.Abelian.FunctorCategory.imageObjIso_inv, ChainComplex.alternatingConst_obj, CategoryTheory.GradedObject.ιMapObjOrZero_eq_zero, CategoryTheory.Preadditive.mono_iff_cancel_zero, CategoryTheory.Limits.inl_pushoutZeroZeroIso_hom, CategoryTheory.Functor.PreservesHomology.preservesKernel, Homotopy.nullHomotopy'_hom, CategoryTheory.Abelian.Pseudoelement.zero_apply, CategoryTheory.Functor.homologySequence_mono_shift_map_mor₂_iff, CategoryTheory.Limits.HasZeroObject.zeroIsoInitial_hom, CategoryTheory.cokernel_zero_of_nonzero_to_simple, CategoryTheory.ShortComplex.zero_τ₂, CategoryTheory.Functor.PreservesZeroMorphisms.map_zero, Rep.FiniteCyclicGroup.resolution.π_f, CategoryTheory.Functor.comp_homologySequenceδ_assoc, CategoryTheory.ShortComplex.LeftHomologyData.liftK_π_eq_zero_of_boundary_assoc, CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel_inr, CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zero_f, CategoryTheory.ComposableArrows.IsComplex.zero', CategoryTheory.DifferentialObject.zero_f, CategoryTheory.Limits.isCokernelEpiComp_desc, CategoryTheory.ShortComplex.hasHomology_of_hasKernel, HomologicalComplex.mapBifunctor₂₃.d₂_eq_zero, CategoryTheory.Limits.KernelFork.mapOfIsLimit_ι, CategoryTheory.ObjectProperty.leftOrthogonal_iff, CategoryTheory.kernelCokernelCompSequence.ι_φ_assoc, CategoryTheory.Preadditive.coforkOfCokernelCofork_pt, CategoryTheory.Pretriangulated.Triangle.zero_hom₂, CategoryTheory.Limits.binaryBiconeOfIsSplitMonoOfCokernel_fst, CategoryTheory.ShortComplex.f_pOpcycles, CategoryTheory.Functor.homologySequence_epi_shift_map_mor₂_iff, CategoryTheory.ShortComplex.isoCyclesOfIsLimit_inv_ι, CategoryTheory.ShortComplex.Splitting.s_r_assoc, CategoryTheory.ShortComplex.opcyclesMap'_zero, CategoryTheory.kernelCokernelCompSequence.φ_π_assoc, HomologicalComplex.liftCycles_homologyπ_eq_zero_of_boundary_assoc, CategoryTheory.mono_to_simple_zero_of_not_iso, CategoryTheory.ShortComplex.f_pOpcycles_assoc, CategoryTheory.ShortComplex.ShortExact.comp_δ_assoc, CochainComplex.HomComplex.Cochain.single_v_eq_zero, CategoryTheory.Limits.cokernel.condition_apply, CategoryTheory.Limits.KernelFork.map_condition_assoc, CategoryTheory.Limits.kernelSubobject_zero, CategoryTheory.Limits.Bicone.ι_of_isLimit
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