Theorems · Theorem · category theory

CategoryTheory.Functor.CommShift.isoZero_hom_app

∀ {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] (F : CategoryTheory.Functor C D) (A : Type u_4) [inst_2 : AddMonoid A]
  [inst_3 : CategoryTheory.HasShift C A] [inst_4 : CategoryTheory.HasShift D A] (X : C),
  (CategoryTheory.Functor.CommShift.isoZero F A).hom.app X =
    CategoryTheory.CategoryStruct.comp (F.map ((CategoryTheory.shiftFunctorZero C A).hom.app X))
      ((CategoryTheory.shiftFunctorZero D A).inv.app (F.obj X))

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

8 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShift