Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {A : Type u'} →
        [inst_1 : CategoryTheory.Category.{v', u'} A] →
          [inst_2 : CategoryTheory.Limits.HasColimitsOfSize.{w, w, v', u'} A] →
            {Φ₁ Φ₂ : J.Point} → (Φ₁ ⟶ Φ₂) → (Φ₂.presheafFiber ⟶ Φ₁.presheafFiber)

The natural transformation on fibers of presheaves that is induced by a morphism of points of a site.

Defined in

Mathlib.CategoryTheory.Sites.Point.Category

Cited by

4 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfSize