Theorems · Definition · category theory

HomologicalComplex.extend.XIso

{ι : Type u_1} →
  {c : ComplexShape ι} →
    {C : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_3} C] →
        [inst_1 : CategoryTheory.Limits.HasZeroObject C] →
          [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
            (K : HomologicalComplex C c) →
              {i : Option ι} → {j : ι} → i = some j → (HomologicalComplex.extend.X K i ≅ K.X j)

The isomorphism X K i ≅ K.X j when i = some j.

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

6 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms