Theorems · Definition · category theory

CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (D : Type u₂) →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        [inst_2 : CategoryTheory.MonoidalCategory D] →
          [inst_3 : CategoryTheory.BraidedCategory D] →
            CategoryTheory.CommMon (CategoryTheory.Functor C D) ≌ CategoryTheory.Functor C (CategoryTheory.CommMon D)

When D is a braided monoidal category, commutative monoid objects in C ⥤ D are the same thing as functors from C into the commutative monoid objects of D.

Defined in

Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory

Cited by

4 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory