Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyData.copy

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S : CategoryTheory.ShortComplex C} →
        (h : S.LeftHomologyData) → {K' H' : C} → (K' ≅ h.K) → (H' ≅ h.H) → S.LeftHomologyData

Given a left homology data h of a short complex S, we can construct another left homology data by choosing another kernel and cokernel that are isomorphic to the ones in h.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

4 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms