Theorems · Definition · category theory

CategoryTheory.Abelian.Ext.bilinearComp

{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 c : ℕ) →
            a + b = c →
              CategoryTheory.Abelian.Ext X Y a →+ CategoryTheory.Abelian.Ext Y Z b →+ CategoryTheory.Abelian.Ext X Z c

The composition of Ext, as a bilinear map.

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.HasExt

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

Cites7

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
AddMonoidHomstatement · cited by 3,230
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.HasExtstatement and proof · cited by 218
CategoryTheory.Abelian.Extstatement and proof · cited by 191
CategoryTheory.Abelian.Ext.compproof · cited by 80
AddMonoidHom.mk'proof · cited by 25

Cited by5

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.Ext.postcompproof · cited by 18
CategoryTheory.Abelian.Ext.precompproof · cited by 15
CategoryTheory.Abelian.Ext.bilinearComp_apply_applystatement and proof · cited by 8
CategoryTheory.Sheaf.H.map_add_applyproof · cited by 0
CategoryTheory.Abelian.Ext.bilinearComp.congr_simpstatement and proof · cited by 0