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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeMar 7th 2021

    Created page.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 10th 2021

    Added to references

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2021

    slightly touched the formatting, e.g. moving remarks on the definition from a subsection at the end of the entry to remarks following the definition

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 10th 2021

    There should be some Isbell duality connection with Osmond’s ideas, no?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2021

    added pointer to

    diff, v6, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 10th 2021

    In Multimonads and multimonadic categories, Diers writes

    We use the notion of multiadjunction developed in [4]

    [4] is

    • Some spectra relative to functors, to appear in J. Pure Appl. Algebra.
    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 10th 2021

    Where Diers then refers us back to

    • Y. Diers, Spectres et localisations relatifs a un foncteur, C.R. Acad. Sci. Paris. Serie A 287 (1978), 985-988.
    • Y. Diers, Familles universelles de morphismes, Ann. Sot. Sci. Bruxelles 93111 (1979) 175-195.
    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMar 10th 2021

    Added a reference to Diers spectrum.

    diff, v8, current

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 11th 2021

    Added a section on multi-monads

    Any functor U:ABU: A\to B which has a left multi-adjoint generates a multi-monad on BB. Categories AA which can be reconstructed from this multi-monad are called multi-monadic (Diers 80).

    Multi-monadic categories on SetSet can be characterized in the following way: they are regular, with connected limits, with coequalizers of coequalizable pairs, their equivalence relations are effective, their forgetful functors preserve coequalizers of equivalence relations and reflect isomorphisms. Unlike monadic categories they need not have products. Examples include local rings, fields, inner spaces, locally compact spaces, locally compact groups, and complete ordered sets. (Diers 80, p.153)

    Seems like important ideas, these ’multi-’ constructs. Why do we hear so little about them?

    diff, v10, current

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 11th 2021

    How about some right multi-adjoints and multi-comonads - any nice cases?

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