Theorems · Definition · category theory
CategoryTheory.HasExt
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.Abelian C] → PropThe property that morphisms between single complexes in arbitrary degrees are w-small
in the derived category.
- Cited by
- 218 results in Mathlib
- Foundations
- Depth 94 from the axioms, rests on 2,467 definitions · 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
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upproof · cited by 1,123
- CochainComplex.singleFunctorproof · cited by 111
- HomologicalComplex.quasiIsoproof · cited by 42
- CategoryTheory.Localization.HasSmallLocalizedShiftedHomproof · cited by 41
Cited by267
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Extstatement and proof · cited by 191
- CategoryTheory.Abelian.Ext.mk₀statement and proof · cited by 94
- CategoryTheory.Abelian.Ext.compstatement and proof · cited by 80
- CategoryTheory.Abelian.Ext.homstatement and proof · cited by 42
- CategoryTheory.ShortComplex.ShortExact.extClassstatement and proof · cited by 36
- CategoryTheory.Abelian.Ext.extstatement and proof · cited by 31
- CategoryTheory.Abelian.Ext.comp_homstatement and proof · cited by 27
- CategoryTheory.HasExt.standardstatement · cited by 22
- CategoryTheory.Abelian.Ext.mk₀_homstatement and proof · cited by 20
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClassstatement and proof · cited by 19
- CategoryTheory.InjectiveResolution.extEquivCohomologyClassstatement and proof · cited by 19
- CategoryTheory.Abelian.Ext.postcompstatement and proof · cited by 18
Showing the 200 most cited of 267.