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    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeDec 5th 2011
    • (edited Dec 5th 2011)

    At comma object, Eduardo Pareja-Tobes put a query box which does not seem to have been ‘answered’. This was some time ago it seems.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 6th 2011

    Thanks! I’ve replied and suggested to continue here.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeDec 6th 2011

    This same person also wrote for us factorization category and twisted arrow category.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 27th 2018

    Six years later, I’m copying the conversation here and deleting the query box:

    Eduardo Pareja-Tobes: Not sure about this but, with the strict definition I think you end up having specified isos all around at the level of morphisms; comma categories as normally defined are comma objects in Cat, but not strict ones (of course they’re equivalent to the strict ones). I remember reading something like this in Makkai-Paré Accessible categories book

    Mike Shulman: As far as I can tell, they are strict. Given DD, functors p:DAp':D\to A, q:DBq':D\to B and a natural transformation σ:fpgq\sigma:f p'\Rightarrow g q', these data specify exactly for every dDd\in D, a triple (p(d),q(d),σ d)(p'(d), q'(d), \sigma_d) which is an object of the comma category. Perhaps you are remembering a related remark about pseudo-pullbacks versus iso-comma objects? (If you post your comments at the nForum, for instance on this discussion, other people will be more likely to see it.)

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