Theorems · Theorem · category theory

CategoryTheory.ShiftedHom.map_naturality_2

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {M : Type u_4} [inst_2 : AddMonoid M]
  [inst_3 : CategoryTheory.HasShift C M] [inst_4 : CategoryTheory.HasShift D M] {X Y : C} {a : M}
  (f : CategoryTheory.ShiftedHom X Y a) {F G : CategoryTheory.Functor C D} (e : F ≅ G) [inst_5 : F.CommShift M]
  [inst_6 : G.CommShift M] [CategoryTheory.NatTrans.CommShift e.hom M],
  (CategoryTheory.ShiftedHom.mk₀ 0 ⋯ (e.hom.app X)).comp
      ((f.map G).comp (CategoryTheory.ShiftedHom.mk₀ 0 ⋯ (e.inv.app Y)) ⋯) ⋯ =
    f.map F

Defined in

Mathlib.CategoryTheory.Shift.ShiftedHom

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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