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  1. I thought it worthwhile to add the view of monoids as strict monoidal categories. This seems missing here.


    diff, v37, current

  2. typo


    diff, v37, current

    • CommentRowNumber3.
    • CommentAuthorRichard Williamson
    • CommentTimeOct 12th 2018
    • (edited Oct 12th 2018)


    • CommentRowNumber4.
    • CommentAuthorPaoloPerrone
    • CommentTimeMay 9th 2019

    Moved examples and other material to the page monoid in a monoidal category’

    diff, v42, current

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 23rd 2020

    Added a reference.

    diff, v43, current

    • CommentRowNumber6.
    • CommentAuthorHurkyl
    • CommentTimeFeb 4th 2022
    • (edited Feb 4th 2022)

    A question on language; isn’t it confusing in a natively homotopy-theoretic context to give unadorned terms like “monoid” a default interpretation that is effectively “… object in Set” rather than “… object in Gpd\infty\! Gpd”?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 4th 2022

    I suppose one might argue that the implicit infinity-category convention should extend to writing “monoid” for A A_\infty-space, but I haven’t heard anyone suggest it before.

    • CommentRowNumber8.
    • CommentAuthorHurkyl
    • CommentTimeFeb 4th 2022

    (note that #6 is meant to be about the HoTT topic page on “Monoid”)

  3. added section about the finite product/sums in a monoid


    diff, v52, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2023

    added pointer to:

    diff, v53, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 12th 2023
    • (edited Aug 12th 2023)

    added historical references:

    Beware that the term “monoid” was first used by

    • Arthur Cayley, Second and Third Memoirs on Skew Surfaces, Otherwise Scrolls, Phil. Trans. (1863 and 1869)

    for certain surfaces, quite unrelated to the modern meaning of the term.

    Instead, what are now called monoids (unital associative magmas) were called groupoids (now clashing with the modern use of groupoid) by

    The modern terminology “monoid” for unital associative magmas is (according to Hollings 2009, p. 529) due to

    For more on the history of the notion:

    It would be good to add more precise pointer to where Bourbaki introduces the terminology.

    diff, v55, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 12th 2023

    while I was at it, I have beautified the typesetting of the classical definition (here)

    diff, v55, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeAug 12th 2023

    Also have given the entry an Idea-section, now here.

    diff, v55, current