Theorems · Theorem · category theory

CategoryTheory.forgetAdjToOver.homEquiv_symm

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {X : C} (Z : CategoryTheory.Over X) (A : C) (f : Z ⟶ (CategoryTheory.toOver X).obj A),
  ((CategoryTheory.forgetAdjToOver X).homEquiv Z A).symm f =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Over.Hom.left f)
      (CategoryTheory.SemiCartesianMonoidalCategory.fst A X)

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Over

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory