Theorems · Theorem · category theory

CategoryTheory.ShortComplex.Exact.lift_f

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {S : CategoryTheory.ShortComplex C} [inst_2 : CategoryTheory.Balanced C] (hS : S.Exact) {A : C} (k : A ⟶ S.X₂)
  (hk : CategoryTheory.CategoryStruct.comp k S.g = 0) [inst_3 : CategoryTheory.Mono S.f],
  CategoryTheory.CategoryStruct.comp (hS.lift k hk) S.f = k

Defined in

Mathlib.Algebra.Homology.ShortComplex.Exact

Cited by

9 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.BalancedCategoryTheory.Mono