Theorems · Inductive type · category theory
CategoryTheory.CategoryWithHomology
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Limits.HasZeroMorphisms C] → PropWe shall say that a category C is a category with homology when all short complexes
have homology.
- Cited by
- 116 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 3 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
Cited by175
Results whose statement or proof uses this declaration.
- HomologicalComplex.homologyFunctorstatement and proof · cited by 70
- HomologicalComplex.quasiIsostatement and proof · cited by 42
- HomotopyCategory.homologyFunctorstatement and proof · cited by 36
- HomotopyCategory.homologyFunctorFactorsstatement and proof · cited by 24
- SSet.homologystatement and proof · cited by 13
- HomologicalComplex.opcyclesFunctorstatement and proof · cited by 12
- HomologicalComplexUpToQuasiIsostatement and proof · cited by 12
- HomotopyCategory.quasiIsostatement and proof · cited by 12
- HomologicalComplexUpToQuasiIso.Qstatement and proof · cited by 11
- ComplexShape.QFactorsThroughHomotopystatement · cited by 11
- HomologicalComplex.cyclesFunctorstatement and proof · cited by 11
- SSet.homologyMapstatement and proof · cited by 9