Theorems · Definition · category theory

CategoryTheory.Abelian.Ext.comp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : CategoryTheory.HasExt C] →
        {X Y Z : C} →
          {a b : ℕ} →
            CategoryTheory.Abelian.Ext X Y a →
              CategoryTheory.Abelian.Ext Y Z b → {c : ℕ} → a + b = c → CategoryTheory.Abelian.Ext X Z c

The composition of Ext.

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by: 80 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.HasExt

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites5

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.Abelianstatement and proof · cited by 1,753
CategoryTheory.HasExtstatement and proof · cited by 218
CategoryTheory.Abelian.Extstatement and proof · cited by 191
CategoryTheory.Localization.SmallShiftedHom.compproof · cited by 12

Cited by87

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.Ext.comp_homstatement · cited by 27
CategoryTheory.Abelian.Ext.comp.congr_simpstatement and proof · cited by 12
CategoryTheory.Abelian.Ext.mk₀_comp_mk₀statement · cited by 10
CategoryTheory.Abelian.Ext.zero_compstatement · cited by 10
CategoryTheory.Abelian.Ext.bilinearComp_apply_applystatement · cited by 8
CategoryTheory.Abelian.Ext.comp_zerostatement · cited by 7
CategoryTheory.Abelian.Ext.zero_homproof · cited by 6
CategoryTheory.Abelian.Ext.mk₀_id_compstatement · cited by 5
CategoryTheory.Abelian.Ext.biprodAddEquivproof · cited by 5
CategoryTheory.Abelian.Ext.comp_assocstatement · cited by 5
CategoryTheory.Abelian.Ext.comp_mk₀_idstatement · cited by 5
CategoryTheory.Abelian.Ext.contravariant_sequence_exact₃statement and proof · cited by 5