Theorems · Theorem · category theory

CategoryTheory.Functor.commShiftIso_comp_inv_app

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [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]
  (F : CategoryTheory.Functor C D) (G : CategoryTheory.Functor D E) {A : Type u_4} [inst_3 : AddMonoid A]
  [inst_4 : CategoryTheory.HasShift C A] [inst_5 : CategoryTheory.HasShift D A] [inst_6 : CategoryTheory.HasShift E A]
  [inst_7 : F.CommShift A] [inst_8 : G.CommShift A] (a : A) (X : C),
  (CategoryTheory.Functor.commShiftIso (F.comp G) a).inv.app X =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.commShiftIso G a).inv.app (F.obj X))
      (G.map ((CategoryTheory.Functor.commShiftIso F a).inv.app X))

Alias of CategoryTheory.Functor.CommShift.comp_commShiftIso_inv_app.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

4 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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