Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.unit_pullbackComp_hom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z)
  [inst_1 : CategoryTheory.ChosenPullbacksAlong f] [inst_2 : CategoryTheory.ChosenPullbacksAlong g]
  [inst_3 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.CategoryStruct.comp f g)],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ChosenPullbacksAlong.mapPullbackAdj (CategoryTheory.CategoryStruct.comp f g)).unit
      ((CategoryTheory.Over.map (CategoryTheory.CategoryStruct.comp f g)).whiskerLeft
        (CategoryTheory.ChosenPullbacksAlong.pullbackComp f g).hom) =
    (CategoryTheory.ChosenPullbacksAlong.mapPullbackAdj (CategoryTheory.CategoryStruct.comp f g)).unit

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlongCategoryTheory.ChosenPullbacksAlongCategoryTheory.ChosenPullbacksAlong