??the "something extra" that a topos model has compared to the underlying model of the corresponding "generalized presheaf topos" as some sort of "continuity" / "cohesion" ???? ??or something ??? ... ??????weird if we're suggesting that this sort of cohesion is _lacking_ in certain algebraic geometry contexts ??? ..... ??particularly if think about relationship between "cohesion" and "flatness" ??????? .... ????...

??hmm, but what about "cohesive property" vs "cohesive structure" vs "cohesive stuff" ??? ... and so forth .... ?????....

??what about the abelian category of sheaves of abelian groups over the real line??? ... ???whether it exhibits "non-toric cohesion" .... ??? ... ????.....

???blecchh, did i get this all backwards (??though a different backwards this time??) again ??? .... ???something about the something extra as some sort of _non_-cohesion ?? ....????..... ????confusion ???? ..... ???....

???maybe something about groupoid vs category here?? ... idea of moore-postnikov factorization idea as way more complicated (and/or less applicable ??? ...) in category case ???? .... ???something about "coalesce" ... ???....

hmm, ok, it really _is_ some sort of extra continuity (??"non-discontinuity" ??..... ???....) up in the space with the "less noticeable" topology, namely the discrete one ... ????... hmmm.... ????.... ???hmmm, something about "local constantness" .... hmmmmmm ..... ???????? ......

???what about something about .... ????local constantness _structure_ and/or _stuff_ ??? .... hmmm.... ????something about .... "drag/transport" ... ???...
????? .... ???...

???hmmm, what about something about ... map from smithereens to original space as maybe both epic and monic???? ... ???.. and so forth .... ????....

???what about something about "analytic continuation" and "morphism that's morally (??or do i mean _genuinely_ ?? ... ???...) mono but restricting along it is injective rather than surjective" and then maybe here "morphism that's morally epi but co-restricting along it is injective rather than surjective" ??????? ..... ???and so forth ??? .... ????.... ???some confusion here ???? ... ??something about ... ??representation ... induce ... ???and so forth ... ???....

??map that's bijective on global points .... ??? ....

???something about ... "expecting a structure but it's actually just a property" ... extendability vs extension ... ??co-extendability vs co-extension ???....

???something about "topology" and "sub-ring" .... ????.... ???something about "restricting a ring homomorphism along a (??"algebraically" ... ???..) "dense" sub-ring" ??? .... ????..... ???wait a minute, isn't "localization" in fact an example of that ??????? ..... ???? .... ????? ..... ????maybe something about "opposite" of bi-morphism as bi-morphism ???? .....

?????........

???something about something extra as classical complements of certain predicates ... ???? ....???...