Theorems · Theorem · category theory

CategoryTheory.IsCommMonObj.ofRepresentableBy

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X : C) (F : CategoryTheory.Functor Cᵒᵖ CommMonCat)
  (α : (F.comp (CategoryTheory.forget CommMonCat)).RepresentableBy X), CategoryTheory.IsCommMonObj X

If X represents a presheaf of commutative monoids, then X is a commutative monoid object.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.CommMon_

Cited by

0 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategory