Theorems · Definition · category theory

CategoryTheory.CommMon.mkIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] →
        {M N : CategoryTheory.CommMon C} →
          (e : M.X ≅ N.X) →
            autoParam (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one e.hom = CategoryTheory.MonObj.one)
                CategoryTheory.CommMon.mkIso._auto_1 →
              autoParam
                  (CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul e.hom =
                    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom e.hom e.hom)
                      CategoryTheory.MonObj.mul)
                  CategoryTheory.CommMon.mkIso._auto_3 →
                (M ≅ N)

Construct an isomorphism of commutative monoid objects by giving an isomorphism between the underlying objects and checking compatibility with unit and multiplication only in the forward direction.

Defined in

Mathlib.CategoryTheory.Monoidal.CommMon_

Cited by

1 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory