Theorems · Definition · category theory

CategoryTheory.Functor.mapMonIdIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      (CategoryTheory.Functor.id C).mapMon ≅ CategoryTheory.Functor.id (CategoryTheory.Mon C)

The identity functor is also the identity on monoid objects.

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

6 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory