Theorems · Definition · category theory

CategoryTheory.SingleFunctors.postcompPostcompIso

{C : Type u_1} →
  {D : Type u_2} →
    {E : Type u_3} →
      {E' : Type u_4} →
        [inst : CategoryTheory.Category.{v_1, u_1} C] →
          [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
            [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
              [inst_3 : CategoryTheory.Category.{v_4, u_4} E'] →
                {A : Type u_5} →
                  [inst_4 : AddMonoid A] →
                    [inst_5 : CategoryTheory.HasShift D A] →
                      [inst_6 : CategoryTheory.HasShift E A] →
                        [inst_7 : CategoryTheory.HasShift E' A] →
                          (F : CategoryTheory.SingleFunctors C D A) →
                            (G : CategoryTheory.Functor D E) →
                              (G' : CategoryTheory.Functor E E') →
                                [inst_8 : G.CommShift A] →
                                  [inst_9 : G'.CommShift A] → (F.postcomp G).postcomp G' ≅ F.postcomp (G.comp G')

The canonical isomorphism (F.postcomp G).postcomp G' ≅ F.postcomp (G ⋙ G').

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

3 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShift