Theorems · Definition · category theory
CategoryTheory.ShortComplex.ShortExact.extClass
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : CategoryTheory.HasExt C] →
{S : CategoryTheory.ShortComplex C} → S.ShortExact → CategoryTheory.Abelian.Ext S.X₃ S.X₁ 1The class in Ext S.X₃ S.X₁ 1 that is attached to a short exact
short complex S in an abelian category.
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upproof · cited by 1,123
- CategoryTheory.ShortComplex.X₁statement and proof · cited by 889
- CategoryTheory.ShortComplex.X₃statement and proof · cited by 876
- CategoryTheory.ShortComplex.fproof · cited by 653
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
- CategoryTheory.HasExtstatement and proof · cited by 218
- CategoryTheory.Abelian.Extstatement · cited by 191
- CategoryTheory.ShortComplex.mapproof · cited by 188
- CochainComplex.mappingConeproof · cited by 181
Cited by39
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.extClass_homstatement · cited by 6
- CategoryTheory.GrothendieckTopology.MayerVietorisSquare.δproof · cited by 5
- CategoryTheory.Abelian.Ext.contravariant_sequence_exact₃statement and proof · cited by 5
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₁statement and proof · cited by 5
- CategoryTheory.Abelian.Ext.contravariant_sequence_exact₁'statement and proof · cited by 4
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₃'statement and proof · cited by 4
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₁'statement and proof · cited by 3
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₃statement and proof · cited by 3
- CategoryTheory.Abelian.Ext.mapExactFunctor_extClassstatement and proof · cited by 2
- CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₃proof · cited by 2
- CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_applystatement and proof · cited by 2
- CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_applystatement and proof · cited by 2