Theorems · Theorem · category theory

CategoryTheory.Localization.SmallHom.shift.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {W : CategoryTheory.MorphismProperty C} {M : Type w'}
  [inst_1 : AddMonoid M] [inst_2 : CategoryTheory.HasShift C M] [inst_3 : W.IsCompatibleWithShift M] {X Y : C}
  [inst_4 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y]
  (f f_1 : CategoryTheory.Localization.SmallHom W X Y),
  f = f_1 →
    ∀ (a : M)
      [inst_5 :
        CategoryTheory.Localization.HasSmallLocalizedHom W ((CategoryTheory.shiftFunctor C a).obj X)
          ((CategoryTheory.shiftFunctor C a).obj Y)],
      f.shift a = f_1.shift a

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.MorphismProperty.IsCompatibleWithShiftCategoryTheory.Localization.HasSmallLocalizedHomCategoryTheory.Localization.HasSmallLocalizedHom