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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 11th 2013

    Added to bimonoid the fact that the category of modules over a bimonoid is monoidal.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2013
    • (edited Jul 11th 2013)

    I added in this section a link to “fiber functor” and then added at the bottome the sentence:

    These relations are known as Tannaka duality for monoids/algebras, see at structure on algebras and their module categories - table.

  1. I added a few string diagrams to the entry.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeJun 16th 2015

    Nice!

    • CommentRowNumber5.
    • CommentAuthorJohn Baez
    • CommentTimeOct 22nd 2020

    Added definition of “bicommutative” bimonoid.

    diff, v15, current

    • CommentRowNumber6.
    • CommentAuthorJohn Baez
    • CommentTimeOct 22nd 2020

    Added information about bimonoids in Rel and FinRel.

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 29th 2022

    Hyperlink to graded bimonoid added.

    diff, v16, current

    • CommentRowNumber8.
    • CommentAuthorGuest
    • CommentTimeJul 29th 2022

    is a bimonoid object in Ab a biring?

    • CommentRowNumber9.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 29th 2022
    • (edited Jul 29th 2022)

    I don’t think so. There is the explicit axioms for a biring in the appendix A of “Representable functors and operations on rings” (D. 0 . TALL and G. C. WRAITH, 1968).

    The only thing true must be that a biring is a monoid object in Ab. It doesn’t seem to be a comonoid object and there is noting like the compatiblity between multiplication and comultiplication which is the most important axiom for a bimonoid.

    Maybe unpacking the explicit diagrams for a biring on the page “biring” would be a good idea.

    • CommentRowNumber10.
    • CommentAuthorGuest
    • CommentTimeJul 29th 2022

    @8 You could probably call them integer bialgebras, as abelian groups are integer modules, and bialgebras are by definition bimonoids in modules.

    • CommentRowNumber11.
    • CommentAuthorJ-B Vienney
    • CommentTime7 days ago

    Added the notion of connected bimonoid.

    diff, v17, current

    • CommentRowNumber12.
    • CommentAuthorJ-B Vienney
    • CommentTime7 days ago

    Added the notion of quasi-bimonoid

    diff, v17, current

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