Theorems · Definition · category theory

HomologicalComplex.xNextIsoSelf

{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) → {i : ι} → ¬c.Rel i (c.next i) → (C.xNext i ≅ C.X i)

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

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