Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.toPresheafFiberNatTrans

{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] →
            [inst_2 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] →
              (X : C) → Φ.fiber.obj X → ((CategoryTheory.evaluation Cᵒᵖ A).obj (Opposite.op X) ⟶ Φ.presheafFiber)

Given a point Φ of a site (C, J), X : C and x : Φ.fiber.obj X, this is the map P.obj (op X) ⟶ Φ.presheafFiber.obj P for any P : Cᵒᵖ ⥤ A as a natural transformation.

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

3 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize