Theorems · Theorem · category theory
HomologicalComplex.homologyMap_id
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{ι : Type u_2} {c : ComplexShape ι} (K : HomologicalComplex C c) (i : ι) [inst_2 : K.HasHomology i],
HomologicalComplex.homologyMap (CategoryTheory.CategoryStruct.id K) i =
CategoryTheory.CategoryStruct.id (K.homology i)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- 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
- HomologicalComplex.homologyMapstatement · cited by 102
- HomologicalComplex.shortComplexFunctorproof · cited by 72
- CategoryTheory.ShortComplex.homologyMap_idproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- groupCohomology.map_idproof · cited by 0
- ContinuousCohomology.map_idproof · cited by 0
- groupHomology.map_idproof · cited by 0
- SSet.homologyMap_idproof · cited by 0