Theorems · Theorem · category theory
Homotopy.homologyMap_eq
∀ {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C] {ι : Type u_3}
{c : ComplexShape ι} {K L : HomologicalComplex C c} {f g : K ⟶ L} (ho : Homotopy f g) (i : ι)
[inst_2 : K.HasHomology i] [inst_3 : L.HasHomology i],
HomologicalComplex.homologyMap f i = HomologicalComplex.homologyMap g i- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Preadditivestatement and proof · cited by 3,309
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- HomologicalComplex.homologystatement · cited by 209
- Homotopystatement and proof · cited by 106
- HomologicalComplex.homologyMapstatement · cited by 102
- Homotopy.toShortComplexproof · cited by 1
- CategoryTheory.ShortComplex.Homotopy.homologyMap_congrproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.SimplicialObject.Homotopy.congr_sSetHomologyMapproof · cited by 2
- SSet.Homotopy.congr_homologyMapproof · cited by 1
- TopCat.Homotopy.congr_homologyMap_singularChainComplexFunctorproof · cited by 0
- CategoryTheory.SimplicialObject.Homotopy.map_homology_eqproof · cited by 0