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    • CommentRowNumber1.
    • CommentAuthorFinnLawler
    • CommentTimeMay 7th 2010

    Created lax-idempotent 2-monad, with some definitions from Kelly–Lack. I think Kock has a couple of others. I’ll add more, like proofs of the equivalence of the definitions, and more on the cocompletion example, later (next week, probably).

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 7th 2010

    Nice, thank you! One quibble: the “idea” description (“algebras over any given object are essentially unique if they exist”) is really the idea of a property-like 2-monad, which is a more general concept than a lax-idempotent one.

    • CommentRowNumber3.
    • CommentAuthorFinnLawler
    • CommentTimeMay 7th 2010

    Right, good point. I’ve edited that section a bit – what do you think of it now?

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeMay 7th 2010

    Looks good.

    • CommentRowNumber5.
    • CommentAuthorFinnLawler
    • CommentTimeMay 13th 2010

    I added some details to the page last night, but for some reason it didn’t turn up in the/my RSS feed, so I thought I’d drop a note here.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 13th 2010

    Thanks!

    I would like to ask you to drop a note here in any case, when you add something. That facilitates interaction a lot more, I think.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeMay 13th 2010

    Nice, thank you! And I second what Urs said.

    • CommentRowNumber8.
    • CommentAuthorFinnLawler
    • CommentTimeMay 13th 2010

    I would like to ask you to drop a note here in any case, when you add something. That facilitates interaction a lot more, I think.

    OK, will do.

    • CommentRowNumber9.
    • CommentAuthorFinnLawler
    • CommentTimeMay 17th 2010

    Right, I think I’m done with this for the time being, unless anyone has any suggestions. I’ve finished off the proof (taken from Kelly & Lack’s paper) of the equivalence of the two usual definitions (unique-2-cell and adjoint-to-unit), and I’ve mentioned colax-idempotence with the fibration 2-monad as an example.

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeMay 17th 2010
    • (edited May 17th 2010)

    Thanks! I added a reference to generalized multicategories, which are one nice source of lax-idempotence.

    Probably property-like structure deserves its own page eventually, where we can discuss property-like 2-monads.