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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 5th 2012

    Ross Tate has pointed out a mismatch in terminology: Kleisli objects and the Grothendieck construction (of a covariant Cat-valued functor) are both asserted to be “lax colimits”, but they are not the same kind of colimit (the 2-cells go in different directions). Thinking about this more, I have concluded that Kleisli objects are lax colimits and the Grothendieck construction is an oplax colimit. I wrote a bit about my reasoning here. But before I go changing all references to the Grothendieck construction to say “oplax colimit”, I thought I should do a sanity check — does this make sense to everyone else?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 6th 2012

    I’d forgotten about it, but this question also came up on MO over 2 years ago.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeOct 11th 2012

    Well, nobody said anything, so I went ahead and changed the few references I could find.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 11th 2012

    It’s okay with me. I was recusing myself from discussing it anyway. :-)