Theorems · Definition · category theory

CategoryTheory.Presheaf.colimitOfRepresentable

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (P : CategoryTheory.Functor Cᵒᵖ (Type (max w v₁))) →
      CategoryTheory.Limits.IsColimit (CategoryTheory.Presheaf.coconeOfRepresentable P)

The cocone with point P given by coconeOfRepresentable is a colimit: that is, we have exhibited an arbitrary presheaf P as a colimit of representables. The result of [MM92], Chapter I, Section 5, Corollary 3.

Defined in

Mathlib.CategoryTheory.Limits.Presheaf

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category