Theorems · Definition · category theory

CategoryTheory.ShortComplex.FunctorEquivalence.unitIso

(J : Type u_1) →
  (C : Type u_2) →
    [inst : CategoryTheory.Category.{v_1, u_1} J] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} C] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          CategoryTheory.Functor.id (CategoryTheory.ShortComplex (CategoryTheory.Functor J C)) ≅
            (CategoryTheory.ShortComplex.FunctorEquivalence.functor J C).comp
              (CategoryTheory.ShortComplex.FunctorEquivalence.inverse J C)

The unit isomorphism of the equivalence ShortComplex.functorEquivalence : ShortComplex (J ⥤ C) ≌ J ⥤ ShortComplex C.

Defined in

Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence

Cited by

7 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms