Theorems · Definition · category theory

CategoryTheory.toOverPullbackIsoToOver

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {X Y : C} →
        (f : Y ⟶ X) →
          [inst_2 : CategoryTheory.ChosenPullbacksAlong f] →
            (CategoryTheory.toOver X).comp (CategoryTheory.ChosenPullbacksAlong.pullback f) ≅ CategoryTheory.toOver Y

A natural isomorphism between the functors toOver Y and toOver X ⋙ pullback f for any morphism f : X ⟶ Y.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Over

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.ChosenPullbacksAlong