Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.presheafFiberCocone

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      (Φ : J.Point) →
        {A : Type u'} →
          [inst_1 : CategoryTheory.Category.{v', u'} A] →
            [CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] →
              (P : CategoryTheory.Functor Cᵒᵖ A) →
                CategoryTheory.Limits.Cocone ((CategoryTheory.CategoryOfElements.π Φ.fiber).op.comp P)

The (colimit) cocone which defines the fiber of a presheaf.

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

2 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize