Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.overMapPullback

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      (A : Type u') →
        [inst_1 : CategoryTheory.Category.{v', u'} A] →
          {X Y : C} →
            (X ⟶ Y) → CategoryTheory.Functor (CategoryTheory.Sheaf (J.over Y) A) (CategoryTheory.Sheaf (J.over X) A)

The pullback functor Sheaf (J.over Y) A ⥤ Sheaf (J.over X) A induced by a morphism f : X ⟶ Y.

Defined in

Mathlib.CategoryTheory.Sites.Over

Cited by

19 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category