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Theorems · Definition · category theory

CategoryTheory.CommMon.toMon

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

A commutative monoid object is a monoid object.

Defined in
Mathlib.CategoryTheory.Monoidal.CommMon_
Cited by
36 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory

Around this declaration

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

CategoryTheory.Functor.mapCommMon · cited by 27Functor.mapCommMonCategoryTheory.CommMon.forget₂Mon · cited by 22CommMon.forget₂MonCategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor · cited by 12CommMonFunctorCategoryEqu…CategoryTheory.Functor.mapCommMonNatIso · cited by 5Functor.mapCommMonNatIsoCategoryTheory.CommMon.homMk · cited by 4CommMon.homMkCategoryTheory.Functor.mapCommMonNatTrans · cited by 4Functor.mapCommMonNatTransCategoryTheory.CommMon.hom_ext · cited by 1CommMon.hom_extCategoryTheory.CommGrp.toMon · cited by 0CommGrp.toMonCategoryTheory.Functor.FullyFaithful.mapCommMon_preimage · cited by 0FullyFaithful.mapCommMon_…CategoryTheory.CommMon.comp_hom · cited by 0CommMon.comp_homCategoryTheory.CommMon.forget_map · cited by 0CommMon.forget_mapCategoryTheory.CommMon.forget₂Mon_map_hom · cited by 0CommMon.forget₂Mon_map_homCategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom · cited by 0CommMonFunctorCategoryEqu…CategoryTheory.CommMon.homMk_hom · cited by 0CommMon.homMk_homCategoryTheory.CommMon.hom_ext_iff · cited by 0CommMon.hom_ext_iffCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.Mon · cited by 465CategoryTheory.MonCategoryTheory.CommMon · cited by 85CategoryTheory.CommMonCategoryTheory.CommMon.X · cited by 50CommMon.XCommMon.toMonCITED BYCITES

Cites6

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Cited by44

Results whose statement or proof uses this declaration.