Theorems · Theorem · category theory

CategoryTheory.Functor.shiftMap_comp

∀ {C : Type u_1} {A : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} A] (F : CategoryTheory.Functor C A) {M : Type u_4} [inst_2 : AddMonoid M]
  [inst_3 : CategoryTheory.HasShift C M] [inst_4 : F.ShiftSequence M] {X Y Z : C} {n : M}
  (f : X ⟶ (CategoryTheory.shiftFunctor C n).obj Y) (g : Y ⟶ Z) (a a' : M) (ha' : n + a = a'),
  F.shiftMap (CategoryTheory.CategoryStruct.comp f ((CategoryTheory.shiftFunctor C n).map g)) a a' ha' =
    CategoryTheory.CategoryStruct.comp (F.shiftMap f a a' ha') ((F.shift a').map g)

Defined in

Mathlib.CategoryTheory.Shift.ShiftSequence

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence