Theorems · Definition · category theory

CategoryTheory.ShortComplex.opcyclesOpIso

{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.op.opcycles ≅ Opposite.op S.cycles

The opcycles in the opposite category of the opposite of a short complex identifies to the cycles of this short complex.

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

8 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology