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Theorems · Definition · category theory

CategoryTheory.CommGrp.toGrp

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      [inst_2 : CategoryTheory.BraidedCategory C] → CategoryTheory.CommGrp C → CategoryTheory.Grp C

A commutative group object is a group object.

Defined in
Mathlib.CategoryTheory.Monoidal.CommGrp_
Cited by
34 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.BraidedCategory

Around this declaration

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

CategoryTheory.Functor.mapCommGrp · cited by 25Functor.mapCommGrpCategoryTheory.CommGrp.forget₂Grp · cited by 19CommGrp.forget₂GrpCategoryTheory.yonedaCommGrpGrpObj · cited by 4CategoryTheory.yonedaComm…CategoryTheory.Functor.mapCommGrpNatIso · cited by 4Functor.mapCommGrpNatIsoCategoryTheory.Functor.mapCommGrpNatTrans · cited by 4Functor.mapCommGrpNatTransCategoryTheory.yonedaCommGrpGrp · cited by 2CategoryTheory.yonedaComm…CategoryTheory.CommGrp.hom_ext · cited by 1CommGrp.hom_extCategoryTheory.CommGrp.mkIso'_hom_hom_hom_hom · cited by 0CommGrp.mkIso'_hom_hom_ho…CategoryTheory.CommGrp.mkIso'_inv_hom_hom_hom · cited by 0CommGrp.mkIso'_inv_hom_ho…CategoryTheory.CommGrp.mkIso_hom_hom_hom_hom · cited by 0CommGrp.mkIso_hom_hom_hom…CategoryTheory.CommGrp.mkIso_inv_hom_hom_hom · cited by 0CommGrp.mkIso_inv_hom_hom…CategoryTheory.CommGrp.toGrp_X · cited by 0CommGrp.toGrp_XCategoryTheory.Functor.FullyFaithful.mapCommGrp_preimage · cited by 0FullyFaithful.mapCommGrp_…CategoryTheory.yonedaCommGrpGrpObj_map · cited by 0CategoryTheory.yonedaComm…CategoryTheory.yonedaCommGrpGrpObj_obj_coe · cited by 0CategoryTheory.yonedaComm…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.BraidedCategory · cited by 779CategoryTheory.BraidedCat…CategoryTheory.Grp · cited by 144CategoryTheory.GrpCategoryTheory.CommGrp · cited by 74CategoryTheory.CommGrpCategoryTheory.CommGrp.X · cited by 39CommGrp.XCommGrp.toGrpCITED BYCITES

Cites6

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

Cited by41

Results whose statement or proof uses this declaration.