?? so is there a classifying topos for "an object for which all restriction maps are invertible" ?? ..... ????? .......

?? "locally has enough global sections" ... ????dependence on action structure ???? ...

?? nice simple example of non-quasicoherent action .... ???? ..... ?? ?? non-universal N-equivariant map from N-set to Z-set .... ????? ..... ?? for example from N to terminal Z-set, or from initial N-set to Z .... ????? .....

?? is it clear whether concept of "quasi-coherent" is at least "site-independent" ??? .... ??? if so then does this maybe automatically imply that it can be expressed in some sort of "topos language" ... ?? .... ????? ...... ??? without necessarily being "geometric" ... ???? .... ???? .....

??? does "quasicoherent" maybe make sense only over _local_ comm ring ?? ... ??? ....

??? consider for example quasicoherent modules in ringed topos given by ... ??? space of real numbers, with ring object "constant" Z ... ???? .... ???? .....

??? identity homomorphism as localization ... ???? .....

?? hmmm .... ??? ....

?? sheaf of lattices vs of semilattices ... ????? ......

?? hmmm.... "comm ring equipped with complement to subobject given by invertibles" ... ???? conservative homomorphisms ?? .... ????? local homomorphisms as special case ???? ..... ??? anti-conservative as maybe not so easy .... ??????? .....

??? sets and surjections ?????? ..... ??? filtered colimits .... ????? ....

??? objects vs morphisms here ???? ...... ?????

?? arbitrary comm ring as "believing itself local" ?? .... ????? .... ???? ... ....... ??? local homomorphisms ....... ????? ......

??? vs .... formal colimits built out of localizations, but with more general morphisms between them .... ????? .......

??? "local localization" ....???? ..... ???? "(??which??) 2 of 3 ..." .... ??? ....

?? having (?? boolean ... ???) complement to invertibles as seeming rather drastic ??? .... ??? anything a bit less drastic ??? ... ??? ....