Theorems · Definition · category theory

CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.inverseObj

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

A functor to the category of monoid objects can be translated as a monoid object in the functor category.

Defined in

Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory

Cited by

6 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategory