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Theorems · Theorem · category theory

HomologicalComplex.congr_hom

∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} {C D : HomologicalComplex V c} {f g : C ⟶ D},
  f = g → ∀ (i : ι), f.f i = g.f i
Defined in
Mathlib.Algebra.Homology.HomologicalComplex
Cited by
13 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicTopology.DoldKan.P_add_Q_f · cited by 3DoldKan.P_add_Q_fAlgebraicTopology.DoldKan.P_f_naturality · cited by 3DoldKan.P_f_naturalityCategoryTheory.ProjectiveResolution.lift_commutes_zero · cited by 2ProjectiveResolution.lift…AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f · cited by 2DoldKan.PInfty_f_add_QInf…CategoryTheory.InjectiveResolution.desc_commutes_zero · cited by 2InjectiveResolution.desc_…CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idem · cited by 1HomologicalComplex.p_idemHomologicalComplex₂.comm_f · cited by 1HomologicalComplex₂.comm_fAlgebraicTopology.DoldKan.map_Hσ · cited by 1DoldKan.map_HσHomologicalComplex.epi_of_epi_f · cited by 1HomologicalComplex.epi_of…CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_d · cited by 1HomologicalComplex.comp_p…CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_f · cited by 1HomologicalComplex.p_comm…CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_d · cited by 1HomologicalComplex.p_comp…HomologicalComplex.mono_of_mono_f · cited by 0HomologicalComplex.mono_o…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex.X · cited by 1839HomologicalComplex.XHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeHomologicalComplex.Hom.f · cited by 845Hom.fHomologicalComplex.congr_homCITED BYCITES

Cites7

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Cited by13

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