Theorems · Definition · category theory

CategoryTheory.Equivalence.CommShift

{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] →
        (E : C ≌ D) →
          (A : Type u_3) →
            [inst_2 : AddMonoid A] →
              [inst_3 : CategoryTheory.HasShift C A] →
                [inst_4 : CategoryTheory.HasShift D A] → [E.functor.CommShift A] → [E.inverse.CommShift A] → Prop

If E : C ≌ D is an equivalence, this expresses the compatibility of CommShift structures on E.functor and E.inverse.

Defined in

Mathlib.CategoryTheory.Shift.Adjunction

Cited by

6 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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