Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback_inv_app_comp_snd

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {Z X : C} (g : Z ⟶ X)
  [inst_1 : CategoryTheory.ChosenPullbacksAlong g] (T : CategoryTheory.Over X),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Over.Hom.left ((CategoryTheory.ChosenPullbacksAlong.pullbackIsoOverPullback g).inv.app T))
      (CategoryTheory.ChosenPullbacksAlong.snd T.hom g) =
    CategoryTheory.Limits.pullback.snd T.hom g

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong

Cited by

1 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlong