Theorems · Definition · category theory

CategoryTheory.Localization.SmallShiftedHom

{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] →
            (X Y : C) → [CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] → M → Type w

The type of morphisms from X to Y⟦m⟧ in the localized category with respect to W : MorphismProperty C that is shrunk to Type w when HasSmallLocalizedShiftedHom.{w} W X Y holds.

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

36 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Localization.HasSmallLocalizedShiftedHom