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nLab > Latest Changes: idempotent monoid in a monoidal category

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDELETED_USER_2018
    • CommentTimeSep 18th 2021
    • (edited Apr 11th 2023)

    [deleted]

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 19th 2021

    Nice!

    I have added hyperlinks to more of the technical term appearing (such Spectra).

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeSep 19th 2021

    Also, should idempotent monoids have a unit?

    When there is no unit, surely the appropriate terminology is “idempotent magma”.

    • CommentRowNumber4.
    • CommentAuthorDELETED_USER_2018
    • CommentTimeSep 19th 2021
    • (edited Apr 11th 2023)

    [deleted]

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeSep 19th 2021

    I agree “idempotent semigroup (object)” seems most suitable when associativity is present. I think “object” can be omitted in this instance, as there ought to be no confusion.

    • CommentRowNumber6.
    • CommentAuthorDELETED_USER_2018
    • CommentTimeSep 20th 2021
    • (edited Apr 11th 2023)

    [deleted]

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeSep 20th 2021

    It’s reasonable to redirect idempotent semigroup to this page, even if it’s mainly about idempotent monoids. I don’t see a problem with terminology like semigroupal category, considering we already have magmoidal category and the like.

    • CommentRowNumber8.
    • CommentAuthorDELETED_USER_2018
    • CommentTimeSep 21st 2021
    • (edited Apr 11th 2023)

    [deleted]

    • CommentRowNumber9.
    • CommentAuthorDELETED_USER_2018
    • CommentTimeSep 26th 2021
    • (edited Apr 11th 2023)

    [deleted]

    • CommentRowNumber10.
    • CommentAuthorncfavier
    • CommentTimeFeb 18th 2024

    Added a note that this is different from the usual definition of an idempotent monoid in algebra.

    diff, v6, current

    • CommentRowNumber11.
    • CommentAuthorP
    • CommentTime7 days ago

    adding redirects for idempotent monoid object

    diff, v7, current

  12. Removed the redirects of idempotent monoid object and idempotent monoid objects from the article and added link to idempotent monoid object which is meant to be about internalizing the algebraic concept.

    Pete Sanders

    diff, v8, current

  13. adding a disambiguation note to the top of the page distinguishing the category theory notion of an “idempotent monoid” and internalizing the algebraic notion of a “idempotent monoid”.

    Pete Sanders

    diff, v8, current

1 to 13 of 13

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