Theorems · Theorem · category theory

CategoryTheory.shiftFunctorComm_inv_app_of_add_eq_zero

∀ {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),
  (CategoryTheory.shiftFunctorComm C m n).inv.app X =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.shiftFunctorCompIsoId C n m ⋯).hom.app X)
      ((CategoryTheory.shiftFunctorCompIsoId C m n hmn).inv.app X)

Defined in

Mathlib.CategoryTheory.Shift.Basic

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddCommMonoidCategoryTheory.HasShift