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nLab > Latest Changes: Surj

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 12th 2021

    Since Inj had a link here, I started something.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 13th 2021

    Hm, it’s not clear that non-standard terminology for a trivial idea needs two separate pages, particularly if neither has anything interesting to say, so far.

    At least the entries should give references for where notation is used this way, if it is. I’d rather expect that if “Inj” is used for any category in the literature, then for subcategories of injective objects, but of course I haven’t made a survey.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 14th 2021

    My attention was drawn to this by someone on Twitter asking for a name for the category, and finding Inj already here

    Let’s see, it’s there on p.720 of

    • John C. Baez, John Foley, Joe Moeller, and Blake S. Pollard, Network Models, Theory and Applications of Categories, Vol. 35, 2020, No. 20, pp 700-744, tac 35-20.

    But others use it for the category whose objects are injective set functions.

    Whatever we do, Inj is a page called by other pages, such as power set.

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeJul 31st 2024

    Added a characterisation and a reference.

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 2nd 2024

    Should that be commutative semigroup rather than commutative monoid? The unit structure $I→MI \to M$ shouldn’t be there if we’re discussing surjections.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeAug 3rd 2024

    Yes, thanks. I copied Paré’s description without thinking about whether it made sense, which was silly of me.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorRodMcGuire
    • CommentTimeAug 3rd 2024

    Added web source to

    • Cole Comfort, A diagrammatic approach to networks of spans and relations, PhD thesis, University of Oxford, 2023, web.

    Was it necessary to delete the reference

    Maybe put it back in with a note that he heavily uses FinSurjFinSurj (which he calls SurjSurj) in it.

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeAug 4th 2024

    I removed it because Paré’s paper had an incorrect assertion about the characterisation of FinSurjFinSurj. Maybe it could be added back in with a remark, though.

1 to 8 of 8

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