Theorems · Theorem · category theory

CategoryTheory.Localization.SmallShiftedHom.equiv_mk

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (W : CategoryTheory.MorphismProperty C) {M : Type w'} [inst_2 : AddMonoid M] [inst_3 : CategoryTheory.HasShift C M]
  [inst_4 : CategoryTheory.HasShift D M] (L : CategoryTheory.Functor C D) [inst_5 : L.IsLocalization W]
  [inst_6 : L.CommShift M] {X Y : C} [inst_7 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] {m : M}
  (f : CategoryTheory.ShiftedHom X Y m),
  (CategoryTheory.Localization.SmallShiftedHom.equiv W L) (CategoryTheory.Localization.SmallShiftedHom.mk W f) = f.map L

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.CommShiftCategoryTheory.Localization.HasSmallLocalizedShiftedHom