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1. • CommentRowNumber1.
   • CommentAuthorThomas Holder
   • CommentTimeMay 13th 2020
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexStarted a page on the geometric theory capturing the concept of a continuous flat functor. <a href="https://ncatlab.org/nlab/revision/theory+of+flat+functors/1">v1</a>, <a href="https://ncatlab.org/nlab/show/theory+of+flat+functors">current</a>

   Started a page on the geometric theory capturing the concept of a continuous flat functor.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 13th 2020
   • (edited May 13th 2020)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIs there something about what it means to be 'continuous' at [[flat functor]], perhaps in the section on [sites](https://ncatlab.org/nlab/show/flat+functor#SiteValuedFunctors)? Oh, does it just mean [[continuous functor]]?

   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?

3. • CommentRowNumber3.
   • CommentAuthorThomas Holder
   • CommentTimeMay 13th 2020
   • PermaLink
   Author: Thomas Holder
   Format: MarkdownItexWell, 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.

   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.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeMay 13th 2020
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItex(It is, to be sure, fairly standard terminology in this area -- although understandably there is potential for confusion.)

   (It is, to be sure, fairly standard terminology in this area – although understandably there is potential for confusion.)