Theorems · Definition · category theory

CategoryTheory.Functor.FullyFaithful.homMulEquiv

{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] → F.FullyFaithful → (X ⟶ M) ≃* (F.obj X ⟶ F.obj M)

Functor.map of a fully faithful monoidal functor as a MulEquiv.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

2 results in Mathlib

Foundations

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

Assumes

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