Theorems · Inductive type · category theory

CategoryTheory.Functor.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] →
        CategoryTheory.Functor C D →
          (A : Type u_6) →
            [inst_2 : AddMonoid A] →
              [CategoryTheory.HasShift C A] → [CategoryTheory.HasShift D A] → Type (max (max u_1 u_6) v_2)

A functor F commutes with the shift by a monoid A if it is equipped with commutation isomorphisms with the shifts by all a : A, and these isomorphisms satisfy coherence properties with respect to 0 : A and the addition in A.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

249 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 5 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShift