Theorems · Theorem · category theory

CategoryTheory.ShortComplex.liftCycles_i

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (S : CategoryTheory.ShortComplex C) {A : C} (k : A ⟶ S.X₂) (hk : CategoryTheory.CategoryStruct.comp k S.g = 0)
  [inst_2 : S.HasLeftHomology], CategoryTheory.CategoryStruct.comp (S.liftCycles k hk) S.iCycles = k

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

18 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology