Theorems · Definition · category theory

CategoryTheory.Monoidal.MonFunctorCategoryEquivalence.functorObjObj

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

A monoid object in a functor category sends any object to a monoid object.

Defined in

Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory

Cited by

5 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonObj