Theorems · Definition · category theory
CategoryTheory.Abelian.Ext
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] → [CategoryTheory.HasExt C] → C → C → ℕ → Type wAn Ext-group in an abelian category C, defined as a Type w when [HasExt.{w} C].
- Cited by
- 191 results in Mathlib
- Foundations
- Depth 95 from the axioms, rests on 2,796 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CategoryTheory.HasExtstatement and proof · cited by 218
- CochainComplex.singleFunctorproof · cited by 111
- HomologicalComplex.quasiIsoproof · cited by 42
- CategoryTheory.Localization.SmallShiftedHomproof · cited by 36
Cited by229
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.mk₀statement · 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 · cited by 36
- CategoryTheory.Abelian.Ext.extstatement and proof · cited by 31
- CategoryTheory.Abelian.Ext.comp_homstatement and proof · cited by 27
- CategoryTheory.InjectiveResolution.extEquivCohomologyClassstatement · cited by 19
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClassstatement · cited by 19
- CategoryTheory.Abelian.Ext.postcompstatement and proof · cited by 18
- CategoryTheory.Abelian.Ext.mapExactFunctorstatement and proof · cited by 15
- CategoryTheory.Abelian.Ext.precompstatement and proof · cited by 15
- CategoryTheory.Abelian.Ext.homEquiv₀statement · cited by 13
Showing the 200 most cited of 229.