Theorems · Theorem · category theory

CategoryTheory.Functor.ShiftSequence.induced.shiftIso.congr_simp

∀ {C : Type u_1} {D : Type u_2} {A : 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} A]
  (L : CategoryTheory.Functor C D) (G : CategoryTheory.Functor C A) (M : Type u_4) [inst_3 : AddMonoid M]
  [inst_4 : CategoryTheory.HasShift C M] [inst_5 : G.ShiftSequence M] (F' : M → CategoryTheory.Functor D A)
  (e' e'_1 : (m : M) → L.comp (F' m) ≅ G.shift m),
  e' = e'_1 →
    ∀ [inst_6 : ((CategoryTheory.Functor.whiskeringLeft C D A).obj L).Full]
      [inst_7 : ((CategoryTheory.Functor.whiskeringLeft C D A).obj L).Faithful] [inst_8 : CategoryTheory.HasShift D M]
      [inst_9 : L.CommShift M] (n a a' : M) (ha' : n + a = a'),
      CategoryTheory.Functor.ShiftSequence.induced.shiftIso L G M F' e' n a a' ha' =
        CategoryTheory.Functor.ShiftSequence.induced.shiftIso L G M F' e'_1 n a a' ha'

Defined in

Mathlib.CategoryTheory.Shift.InducedShiftSequence

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequenceCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.HasShiftCategoryTheory.Functor.CommShift