Theorems · Theorem · category theory

CategoryTheory.SingleFunctors.lift.shiftIso.congr_simp

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{u_5, u_1} C]
  [inst_1 : CategoryTheory.Category.{u_6, u_2} D] [inst_2 : CategoryTheory.Category.{u_7, u_3} E] {A : Type u_4}
  [inst_3 : AddMonoid A] [inst_4 : CategoryTheory.HasShift D A] [inst_5 : CategoryTheory.HasShift E A]
  {F : CategoryTheory.SingleFunctors C E A} {G : CategoryTheory.Functor D E} [inst_6 : G.CommShift A] [inst_7 : G.Full]
  [inst_8 : G.Faithful] {Φ : A → CategoryTheory.Functor C D} (hΦ hΦ_1 : (a : A) → (Φ a).comp G ≅ F.functor a),
  hΦ = hΦ_1 →
    ∀ (n a a' : A) (h : n + a = a'),
      CategoryTheory.SingleFunctors.lift.shiftIso hΦ n a a' h =
        CategoryTheory.SingleFunctors.lift.shiftIso hΦ_1 n a a' h

Defined in

Mathlib.CategoryTheory.Shift.SingleFunctorsLift

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.FullCategoryTheory.Functor.Faithful