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- Cited by
- 13 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.Hom.fstatement and proof · cited by 845
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.P_add_Q_fproof · cited by 3
- AlgebraicTopology.DoldKan.P_f_naturalityproof · cited by 3
- CategoryTheory.ProjectiveResolution.lift_commutes_zeroproof · cited by 2
- AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_fproof · cited by 2
- CategoryTheory.InjectiveResolution.desc_commutes_zeroproof · cited by 2
- CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_idemproof · cited by 1
- HomologicalComplex₂.comm_fproof · cited by 1
- AlgebraicTopology.DoldKan.map_Hσproof · cited by 1
- HomologicalComplex.epi_of_epi_fproof · cited by 1
- CategoryTheory.Idempotents.Karoubi.HomologicalComplex.comp_p_dproof · cited by 1
- CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comm_fproof · cited by 1
- CategoryTheory.Idempotents.Karoubi.HomologicalComplex.p_comp_dproof · cited by 1