Theorems · Theorem · category theory
CategoryTheory.Abelian.Ext.zero_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : CategoryTheory.HasExt C] (X : C) {Y Z : C} (n : ℕ) {m : ℕ} (β : CategoryTheory.Abelian.Ext Y Z m) (p : ℕ)
(h : n + m = p), CategoryTheory.Abelian.Ext.comp 0 β h = 0- Cited by
- 10 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 by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.add_homproof · cited by 4
- CategoryTheory.Retract.hasInjectiveDimensionLTproof · cited by 2
- CategoryTheory.Limits.IsZero.hasProjectiveDimensionLT_zeroproof · cited by 2
- CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₁proof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₃proof · cited by 1
- CategoryTheory.Abelian.Ext.postcomp_smul_id_eq_zero_of_mem_annihilatorproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.extClass_comp_assocproof · cited by 0
- CategoryTheory.ShortComplex.ShortExact.hasInjectiveDimensionLT_X₂proof · cited by 0
- CategoryTheory.hasProjectiveDimensionLT_of_enoughInjectivesproof · cited by 0
- CategoryTheory.ShortComplex.ShortExact.comp_extClass_assocproof · cited by 0