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Theorems · Definition · category theory

CategoryTheory.CommMon.X

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

The underlying object in the ambient monoidal category

Defined in
Mathlib.CategoryTheory.Monoidal.CommMon_
Cited by
50 results in Mathlib
Foundations
Depth 4 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.toMon · cited by 36CommMon.toMonCategoryTheory.Functor.mapCommMonCompIso · cited by 6Functor.mapCommMonCompIsoCategoryTheory.Functor.mapCommMonIdIso · cited by 6Functor.mapCommMonIdIsoCategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj · cited by 6EquivLaxBraidedFunctorPUn…CategoryTheory.Functor.mapCommMonFunctor · cited by 3Functor.mapCommMonFunctorCategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.unitIso · cited by 3CommMonFunctorCategoryEqu…CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso · cited by 3EquivLaxBraidedFunctorPUn…CategoryTheory.CommMon.mkIso · cited by 1CommMon.mkIsoCategoryTheory.CommGrp.toCommMon_X · cited by 0CommGrp.toCommMon_XCategoryTheory.CommMon.mkIso.congr_simp · cited by 0mkIso.congr_simpCategoryTheory.CommMon.forget_obj · cited by 0CommMon.forget_objCategoryTheory.CommMon.forget₂Mon_obj_X · cited by 0CommMon.forget₂Mon_obj_XCategoryTheory.CommMon.forget₂Mon_obj_mul · cited by 0CommMon.forget₂Mon_obj_mulCategoryTheory.CommMon.forget₂Mon_obj_one · cited by 0CommMon.forget₂Mon_obj_oneCategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.counitIso_hom_app_app_hom_hom · cited by 0CommMonFunctorCategoryEqu…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.CommMon · cited by 85CategoryTheory.CommMonCommMon.XCITED BYCITES

Cites4

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

Cited by60

Results whose statement or proof uses this declaration.