Theorems · Theorem · category theory

CategoryTheory.isCommMonObj_iff_isMulCommutative

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (M : C) [inst_2 : CategoryTheory.MonObj M] [inst_3 : CategoryTheory.BraidedCategory C],
  CategoryTheory.IsCommMonObj M ↔ ∀ (X : C), IsMulCommutative (X ⟶ M)

A monoid object M is commutative if and only if X ⟶ M is commutative for all X.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Mon

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObjCategoryTheory.BraidedCategory