Theorems · Theorem · category theory

CategoryTheory.Functor.CommShift.OfComp.iso.congr_simp

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D E} {H : CategoryTheory.Functor C E}
  (e e_1 : F.comp G ≅ H),
  e = e_1 →
    ∀ [inst_3 : G.Full] [inst_4 : G.Faithful] {A : Type u_5} [inst_5 : AddMonoid A]
      [inst_6 : CategoryTheory.HasShift C A] [inst_7 : CategoryTheory.HasShift D A]
      [inst_8 : CategoryTheory.HasShift E A] [inst_9 : G.CommShift A] [inst_10 : H.CommShift A] (a : A),
      CategoryTheory.Functor.CommShift.OfComp.iso e a = CategoryTheory.Functor.CommShift.OfComp.iso e_1 a

Defined in

Mathlib.CategoryTheory.Shift.CommShift

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShift