?? topos of filteredly cocontinuous set-valued frs .... ??? ... "flatness axioms" and "higher flatness axioms" .... ??? non-coherent or worse ??? .... ???? .... ?? "flat" vs "filtered" ..... ?? "filtered" (?? ...)expressed in terms of cover ???? ..... ??? level slip concerning property of diagram schemes vs property of preserving colimits of those shapes .... ???? but then ... ??? certain patterns that _do_ recur (?? ...) here .... ???? "object st homming from it preserves colimits of given kind" .... ??? situations where this corresponds to not being a colimit of that kind in any non-trivial (?? ...) way ... ????? ..... ?? then also .... ??? "flat" as related to "filtered" ....... ????? ...... ((higher ...) flatness/filteredness axioms .... ??? non-coherent or worse ??? ....) ... ??? when tensoring with preserves limits vs when homming from preserves colimits ???? .... ??? ... suggestive .... ??? .... ??? try to straighten out .... ??? ....

?? diaconescu's thm here ... ??? still not very "internal" approach, though .... ???? .....

?? freyd's "extension logic" (?? ...) here (?? ...) .... ????? ..... ?? relationship to "grothendieck topology" and "cover" ??? ..... ?? filteredness (?? for example ?? ...) .... ???? .... ?? categorification .... ???? higher (?? more than one way ???? .... ???? ....) topos ... ??? ..... ???? ... "arbitrary length quantifier alternation strings" .... vs "geometric" ??? ... ????? ......