filteredly cocomplete (??small ?? ...) category and special grothendieck topology on it... ??and how to recover this site from its topos...
(hmmm, that might be screwed up .... maybe instead of sheaves for grothendieck topology we want set-valued functors preserving filtered colimits ... or something ... ??anyway, maybe with this one minor/major little change, the basic ideas can still go through ... ???....)
free vs non-free filteredly cocomplete category... ??something about the above topos as just a presheaf topos in the free case ... ??...
motivation for above in terms of accidental topos of toric variety... and so forth ...
??maybe something about "toric model" idea ??? .... and so forth ...
??maybe warning about ... ???not reallty getting to the "interesting" topos stuff yet .... ???want to get to catalog, but ... ??....
??idea of collaborating with alex?? ...
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