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Theorems · Inductive type · category theory

CategoryTheory.CommMon

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

A commutative monoid object internal to a monoidal category.

Defined in
Mathlib.CategoryTheory.Monoidal.CommMon_
Cited by
85 results in Mathlib
Foundations
Depth 3 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.CommMon.X · cited by 50CommMon.XCategoryTheory.CommMon.toMon · cited by 36CommMon.toMonCategoryTheory.Functor.mapCommMon · cited by 27Functor.mapCommMonCategoryTheory.CommMon.forget₂Mon · cited by 22CommMon.forget₂MonCategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.functor · cited by 12CommMonFunctorCategoryEqu…CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse · cited by 12CommMonFunctorCategoryEqu…CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided · cited by 11EquivLaxBraidedFunctorPUn…CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon · cited by 11EquivLaxBraidedFunctorPUn…CategoryTheory.Functor.mapCommMonCompIso · cited by 6Functor.mapCommMonCompIsoCategoryTheory.Functor.mapCommMonIdIso · cited by 6Functor.mapCommMonIdIsoCategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj · cited by 6EquivLaxBraidedFunctorPUn…CategoryTheory.Functor.mapCommMonNatIso · cited by 5Functor.mapCommMonNatIsoCategoryTheory.CommMon.trivial · cited by 5CommMon.trivialCategoryTheory.Monoidal.commMonFunctorCategoryEquivalence · cited by 4Monoidal.commMonFunctorCa…CategoryTheory.Equivalence.mapCommMon · cited by 4Equivalence.mapCommMonCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.CommMonCITED BYCITES

Cites3

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

Cited by128

Results whose statement or proof uses this declaration.