Theorems · Theorem · category theory

CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero_assoc

∀ {C : Type u} {A : Type u_1} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : AddCommMonoid A]
  [inst_2 : CategoryTheory.HasShift C A] (m n : A) (hmn : m + n = 0) (X : C) {Z : C}
  (h : (CategoryTheory.shiftFunctor C n).obj ((CategoryTheory.shiftFunctor C m).obj X) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorComm C m n).inv.app X) h =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorCompIsoId C n m ⋯).hom.app X)
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorCompIsoId C m n hmn).inv.app X) h)

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddCommMonoidCategoryTheory.HasShift