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Dec 11, 2017 at 19:00 comment added Tim Campion Yes, it's definitely confusing. For me, just writing "a map out of the pullback $c \times_d c'$" above felt wrong somehow, but there it is!
Dec 11, 2017 at 10:57 comment added Philippe Gaucher I did not know this notion of trifibration and the nLab page is a bit confusing: $E^{op}$ is not the opposite category.
Dec 10, 2017 at 23:01 history edited Tim Campion CC BY-SA 3.0
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Dec 10, 2017 at 22:20 comment added John Berman Great! I had forgotten all about this construction, and never seen the bit on trifibrations. I think an LCC functor should be one that preserves pullbacks and dependent products.
Dec 10, 2017 at 17:43 history answered Tim Campion CC BY-SA 3.0