Theorems · Definition · category theory

CategoryTheory.Localization.HasSmallLocalizedShiftedHom

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    CategoryTheory.MorphismProperty C →
      (M : Type w') → [inst_1 : AddMonoid M] → [CategoryTheory.HasShift C M] → C → C → Prop

Given objects X and Y in a category C, this is the property that all the types of morphisms from X⟦a⟧ to Y⟦b⟧ are w-small in the localized category with respect to a class of morphisms W.

Defined in

Mathlib.CategoryTheory.Localization.SmallShiftedHom

Cited by

41 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryAddMonoidCategoryTheory.HasShift