Theorems · Definition · category theory

HomologicalComplex.singleObjXSelf

{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) → ((HomologicalComplex.single V c j).obj A).X j ≅ A

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

Defined in

Mathlib.Algebra.Homology.Single

Cited by

53 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq