Theorems · Inductive type · category theory

CategoryTheory.NatTrans.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] →
        {F₁ F₂ : CategoryTheory.Functor C D} →
          (F₁ ⟶ F₂) →
            (A : Type u_5) →
              [inst_2 : AddMonoid A] →
                [inst_3 : CategoryTheory.HasShift C A] →
                  [inst_4 : CategoryTheory.HasShift D A] → [F₁.CommShift A] → [F₂.CommShift A] → Prop

If τ : F₁ ⟶ F₂ is a natural transformation between two functors which commute with a shift by an additive monoid A, this typeclass asserts a compatibility of τ with these shifts.

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

41 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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