Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.Point.presheafFiber_map_shrinkYoneda_map_shrinkYonedaCompPresheafFiberIso_inv_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} (Φ : J.Point)
  [inst_1 : CategoryTheory.LocallySmall.{w, v, u} C] {X Y : C} (f : X ⟶ Y) (x : Φ.fiber.obj X),
  (CategoryTheory.ConcreteCategory.hom (Φ.presheafFiber.map (CategoryTheory.shrinkYoneda.{w, v, u}.map f)))
      ((CategoryTheory.ConcreteCategory.hom (Φ.shrinkYonedaCompPresheafFiberIso.inv.app X)) x) =
    (CategoryTheory.ConcreteCategory.hom (Φ.toPresheafFiber X x (CategoryTheory.shrinkYoneda.{w, v, u}.obj Y)))
      (CategoryTheory.shrinkYonedaObjObjEquiv.symm f)

Defined in

Mathlib.CategoryTheory.Sites.Point.Basic

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.LocallySmall