Theorems · Definition · category theory

CategoryTheory.Over.pullback

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} →
      (f : X ⟶ Y) →
        [CategoryTheory.Limits.HasPullbacksAlong f] →
          CategoryTheory.Functor (CategoryTheory.Over Y) (CategoryTheory.Over X)

In a category with pullbacks, a morphism f : X ⟶ Y induces a functor Over Y ⥤ Over X, by pulling back a morphism along f.

Defined in

Mathlib.CategoryTheory.Comma.Over.Pullback

Cited by

53 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksAlong