Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.presheafFiberDesc

{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] →
              {P : CategoryTheory.Functor Cᵒᵖ A} →
                {T : A} →
                  (φ : (X : C) → Φ.fiber.obj X → (P.obj (Opposite.op X) ⟶ T)) →
                    autoParam
                        (∀ ⦃X Y : C⦄ (f : X ⟶ Y) (x : Φ.fiber.obj X),
                          CategoryTheory.CategoryStruct.comp (P.map f.op) (φ X x) =
                            φ Y ((CategoryTheory.ConcreteCategory.hom (Φ.fiber.map f)) x))
                        _auto_48✝ →
                      (Φ.presheafFiber.obj P ⟶ T)

Constructor for morphisms from the fiber of a presheaf.

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

7 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize