Theorems · Definition · category theory

CategoryTheory.toOverIteratedSliceForwardIsoPullback

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

The functor pullback f : Over X ⥤ Over Y is naturally isomorphic to toOver : Over X ⥤ Over (Over.mk f) post-composed with the iterated slice equivalence Over (Over.mk f) ⥤ Over Y.

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Over

Cited by

2 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacks