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Jun 30, 2017 at 16:44 comment added Mike Shulman By the way, arxiv.org/abs/1301.3191 may be helpful (see in particular 10.7 and 10.8), although I don't think it exactly answers your questions as posed without a bit more work.
Apr 13, 2017 at 12:19 history edited CommunityBot
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Apr 12, 2014 at 23:36 comment added Mike Shulman As for your original questions, I think the answers are "of course", but I don't know whether anyone has sat down and written out the details. (-:
Apr 12, 2014 at 23:33 comment added Mike Shulman There is a Gray tensor product for bicategories. However, at least if you're talking about the pseudo version of the Gray tensor product, it is equivalent to the cartesian product (in the appropriately weak sort of "equivalence" for bicategories, a.k.a. "biequivalence"). Thus, if you're talking about pseudofunctors (as you usually are when considering bicategories), there's no point to using the Gray tensor product instead of the cartesian product.
Apr 12, 2014 at 9:41 comment added Ma Ming @AdamGal Gray tensor product for bicategories? It seems that Gray tensor product is for 2-categories (I remember that the Cartesian product of bicategories is not closed but weak closed.)
Apr 10, 2014 at 19:49 comment added Adam Gal A small note: The original functor you consider should be a bi-functor, i.e. a functor from the Gray tensor. Probably your construction will yield two limits which are isomorphic to the limit of the functor from the tensor.
Apr 10, 2014 at 15:18 history edited Ricardo Andrade CC BY-SA 3.0
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Apr 10, 2014 at 13:54 history edited Ma Ming CC BY-SA 3.0
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Apr 8, 2014 at 18:36 history asked Ma Ming CC BY-SA 3.0