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Is there something about what it means to be ’continuous’ at flat functor, perhaps in the section on sites?
Oh, does it just mean continuous functor?
Well, the notion of “continuous” is the one where a flat functor $\mathcal{C}\to\mathcal{E}$ is said to be continuous for $J$ if it sends covering sieves to epimorphic families (e.g. Moerdijk-MacLane p.393f). I guess this terminology is supposed to show up somewhere on the nLab. Once I have finished the missing two axioms I’ll do some further linking at least with some geometrico- logically leaning pages.
(It is, to be sure, fairly standard terminology in this area – although understandably there is potential for confusion.)
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