Theorems · Theorem · category theory
CategoryTheory.Abelian.Ext.comp_zero
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : CategoryTheory.HasExt C] {X Y : C} {n : ℕ} (α : CategoryTheory.Abelian.Ext X Y n) (Z : C) (m p : ℕ)
(h : n + m = p), α.comp 0 h = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CategoryTheory.HasExtstatement and proof · cited by 218
- CategoryTheory.Abelian.Extstatement and proof · cited by 191
- HasDerivedCategoryproof · cited by 190
- CategoryTheory.Abelian.Ext.compstatement · cited by 80
- DerivedCategory.singleFunctorproof · cited by 78
- CategoryTheory.Abelian.Ext.homproof · cited by 42
- HasDerivedCategory.standardproof · cited by 42
- CategoryTheory.ShiftedHom.comp.congr_simpproof · cited by 37
- CategoryTheory.Abelian.Ext.extproof · cited by 31
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.zero_homproof · cited by 6
- CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₃proof · cited by 2
- CategoryTheory.Retract.hasProjectiveDimensionLTproof · cited by 2
- CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₁proof · cited by 1
- CategoryTheory.Limits.IsZero.hasInjectiveDimensionLT_zeroproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₂proof · cited by 0
- CategoryTheory.hasInjectiveDimensionLT_of_enoughProjectivesproof · cited by 0