Theorems · Theorem · category theory

CategoryTheory.SingleFunctors.Hom.comm_assoc

∀ {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} (self : F.Hom G) (n a a' : A)
  (ha' : n + a = a') {Z : CategoryTheory.Functor C D} (h : G.functor a ⟶ Z),
  CategoryTheory.CategoryStruct.comp (F.shiftIso n a a' ha').hom (CategoryTheory.CategoryStruct.comp (self.hom a) h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.whiskerRight (self.hom a') (CategoryTheory.shiftFunctor D n))
      (CategoryTheory.CategoryStruct.comp (G.shiftIso n a a' ha').hom h)

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctors

Cited by

0 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShift