Theorems · Definition · category theory

HomologicalComplex.singleObjXIsoOfEq

{V : Type u} →
  [inst : CategoryTheory.Category.{v, u} V] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject V] →
        {ι : Type u_1} →
          [inst_3 : DecidableEq ι] →
            (c : ComplexShape ι) →
              (j : ι) → (A : V) → (i : ι) → i = j → (((HomologicalComplex.single V c j).obj A).X i ≅ A)

The object in degree i of (single V c h).obj A is just A when i = j.

Defined in

Mathlib.Algebra.Homology.Single

Cited by

6 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq