Theorems · Definition · category theory

HomologicalComplex.xPrevIsoSelf

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
        {c : ComplexShape ι} → (C : HomologicalComplex V c) → {j : ι} → ¬c.Rel (c.prev j) j → (C.xPrev j ≅ C.X j)

If there is no i so c.Rel i j, then C.xPrev j is isomorphic to C.X j.

Defined in

Mathlib.Algebra.Homology.HomologicalComplex

Cited by

3 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms