Theorems · Definition · category theory

CategoryTheory.MorphismProperty.presheaf

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    CategoryTheory.MorphismProperty C → CategoryTheory.MorphismProperty (CategoryTheory.Functor Cᵒᵖ (Type v₁))

Given a morphism property P in a category C, a morphism f : F ⟶ G of presheaves in the category Cᵒᵖ ⥤ Type v satisfies the morphism property P.presheaf iff: * The morphism is representable. * For any morphism g : F.obj a ⟶ G, the property P holds for any represented pullback of f by g. This is implemented as a special case of the more general notion of P.relative, to the case when the functor F is yoneda.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Representable

Cited by

17 results in Mathlib

Foundations

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

Assumes

CategoryTheory.Category