Mathlib Map

Theorems · Definition · category theory

CategoryTheory.CommMon.trivial

(C : Type u₁) →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] → CategoryTheory.CommMon C

The trivial commutative monoid object. We later show this is initial in CommMon C.

Defined in
Mathlib.CategoryTheory.Monoidal.CommMon_
Cited by
5 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon · cited by 11EquivLaxBraidedFunctorPUn…CategoryTheory.CommMon.trivial_mon_one · cited by 0CommMon.trivial_mon_oneCategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map · cited by 0EquivLaxBraidedFunctorPUn…CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj · cited by 0EquivLaxBraidedFunctorPUn…CategoryTheory.CommMon.trivial_X · cited by 0CommMon.trivial_XCategoryTheory.CommMon.trivial_mon_mul · cited by 0CommMon.trivial_mon_mulCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.MonoidalCategoryStruct.tensorUnit · cited by 1384MonoidalCategoryStruct.te…CategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.CommMon · cited by 85CategoryTheory.CommMonCommMon.trivialCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.