Theorems · Definition · category theory

CategoryTheory.SingleFunctors.isoMk

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {A : Type u_5} →
          [inst_2 : AddMonoid A] →
            [inst_3 : CategoryTheory.HasShift D A] →
              {F G : CategoryTheory.SingleFunctors C D A} →
                (iso : (a : A) → F.functor a ≅ G.functor a) →
                  (∀ (n a a' : A) (ha' : n + a = a'),
                      CategoryTheory.CategoryStruct.comp (F.shiftIso n a a' ha').hom (iso a).hom =
                        CategoryTheory.CategoryStruct.comp
                          (CategoryTheory.Functor.whiskerRight (iso a').hom (CategoryTheory.shiftFunctor D n))
                          (G.shiftIso n a a' ha').hom) →
                    (F ≅ G)

Construct an isomorphism in SingleFunctors C D A by giving level-wise isomorphisms and checking compatibility only in the forward direction.

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift