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 CA 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
- CategoryTheory.Monstatement · cited by 465
- CategoryTheory.CommMonstatement and proof · cited by 85
- CategoryTheory.CommMon.Xproof · cited by 50
Cited by44
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.mapCommMonproof · cited by 27
- CategoryTheory.CommMon.forget₂Monproof · cited by 22
- CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functorproof · cited by 12
- CategoryTheory.Functor.mapCommMonNatIsoproof · cited by 5
- CategoryTheory.CommMon.homMkstatement and proof · cited by 4
- CategoryTheory.Functor.mapCommMonNatTransproof · cited by 4
- CategoryTheory.CommMon.hom_extstatement · cited by 1
- CategoryTheory.CommGrp.toMonproof · cited by 0
- CategoryTheory.Functor.FullyFaithful.mapCommMon_preimagestatement · cited by 0
- CategoryTheory.CommMon.comp_homstatement · cited by 0
- CategoryTheory.CommMon.forget_mapstatement · cited by 0
- CategoryTheory.CommMon.forget₂Mon_map_homstatement · cited by 0