Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorPaoloPerrone
    • CommentTimeOct 28th 2019

    I feel that, while the concept of algebra over a monad is of course an instance of the more general module over a monad, it could benefit from having its own dedicated page, with motivation from other fields and dedicated examples.

    If I get a green light from enough people here, I can create the page myself (and replace the redirection by links both ways).

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 29th 2019
    • (edited Oct 29th 2019)

    Currently, the point of view of the entry is that “algebra for a monad” is synonymous with “module over a monad” at least or especially for monads in Cat, since in this case their modules literally are algebras in the sense of universal algebra.

    I suppose what you are after is the concept of monoid objects in categories of modules over a monad?

    I’d think this should definitely be on a page of its own, and then there ought to be a paragraph alerting the reader of the trouble with the terminology.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeOct 29th 2019

    I suspect that Paolo’s point was instead to have a separate page for algebras in Cat with domain 1, so that people can read about those without having to think about bicategories. I think that’s a good idea.

    • CommentRowNumber4.
    • CommentAuthorPaoloPerrone
    • CommentTimeOct 29th 2019

    Yes, I meant exactly what Mike has said.

    (Of course, what Urs has said should have a page too.)

    • CommentRowNumber5.
    • CommentAuthorPaoloPerrone
    • CommentTimeJan 14th 2020

    I’ll proceed in the next days.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)