Theorems · Definition · category theory

CategoryTheory.ShortComplex.toCycles

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) → [inst_2 : S.HasLeftHomology] → S.X₁ ⟶ S.cycles

The "boundaries" map S.X₁ ⟶ S.cycles. (Note that in this homology API, we make no use of the "image" of this morphism, which under some categorical assumptions would be a subobject of S.X₂ contained in S.cycles.)

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

47 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology