Theorems · Theorem · category theory

CategoryTheory.ShortComplex.Exact.comp_descToInjective

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  {S : CategoryTheory.ShortComplex C} (hS : S.Exact) {J : C} (f : S.X₂ ⟶ J) [inst_2 : CategoryTheory.Injective J]
  (hf : CategoryTheory.CategoryStruct.comp S.f f = 0),
  CategoryTheory.CategoryStruct.comp S.g (hS.descToInjective f hf) = f

Defined in

Mathlib.Algebra.Homology.ShortComplex.Exact

Cited by

6 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Injective