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Jun 18, 2018 at 20:52 comment added David Roberts For the long version of this answer, see math.harvard.edu/~lurie/278x.html :-)
Jan 20, 2015 at 23:38 comment added Mike Shulman Isn't a geometric morphism usually denoted as going in the direction of its direct image functor, so $\pi : \mathcal{X}\to\mathcal{S}$?
Jan 20, 2015 at 15:22 comment added David Corfield Thank you very much! This seems related to the hyperdoctrine concept: ncatlab.org/nlab/show/hyperdoctrine.
Jan 20, 2015 at 15:17 vote accept David Corfield
Jan 20, 2015 at 14:51 history answered Jacob Lurie CC BY-SA 3.0