Theorems · Definition · category theory

HomologicalComplex.singleCompEvalIsoSelf

(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) →
                (HomologicalComplex.single V c j).comp (HomologicalComplex.eval V c j) ≅ CategoryTheory.Functor.id V

The natural isomorphism single V c j ⋙ eval V c j ≅ 𝟭 V.

Defined in

Mathlib.Algebra.Homology.Single

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq