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    • CommentRowNumber1.
    • CommentAuthorSam Staton
    • CommentTimeAug 14th 2019

    expand with definition

    diff, v3, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 15th 2019

    So, for some examples, closure operators for 2\mathbf{2}, presumably. Anything interesting for metric spaces?

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeAug 15th 2019

    reference

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorSam Staton
    • CommentTimeAug 15th 2019
    • (edited Aug 15th 2019)
    Yes, closure operators would be an example, and I notice that the Kleisli presentation is indeed a known slick way of describing closure operators, which is quite nice. Not sure about the metric example, good question. What role do adjunctions play in the metric setting? Sorry if I have forgotten.

    Another example is that people often use cpo-enriched monads in CS for the semantics of iteration.
    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 15th 2019

    Added the example of closure operator, and linked to enriched adjunction.

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 19th 2019

    Is there a standard reference for the enriched version of things like Kleisli, Eilenberg-Moore categories, monads as lax 2-functors etc.?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeAug 20th 2019

    Well, from one perspective there’s not much to say, since VCatV Cat is a 2-category and all of that is 2-categorical abstract nonsense. But I think there’s some particular discussion of enriched monads in Dubuc’s book Kan Extensions in Enriched Category Theory.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 20th 2019

    Thanks!

    diff, v7, current

  1. remove redundant ZZ in definition.

    Sandro Stucki

    diff, v9, current

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