Theorems · Theorem · category theory

CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v, u_1} C]
  [inst_1 : CategoryTheory.CartesianMonoidalCategory C] [inst_2 : CategoryTheory.Category.{w, u_2} D]
  [inst_3 : CategoryTheory.CartesianMonoidalCategory D] {M X : C} [inst_4 : CategoryTheory.MonObj M]
  (F : CategoryTheory.Functor C D) [inst_5 : F.Monoidal] (hF : F.FullyFaithful) (f : F.obj X ⟶ F.obj M),
  (CategoryTheory.Functor.FullyFaithful.homMulEquiv F hF).symm f = hF.preimage f

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.Functor.Monoidal