??so what about this quasitopos analogy (or something) we seem to be running into here??

???something about... ??topos has subobject classifier but pulling back along geometric morphism doesn't preserve it, maybe analogous to good tensor category has kernels but pulling back along geometric morphism doesn't preserve it... ???or something?? .... ??something about kernels and "obstruction theory" ... ?????hmmm.... ????....

??so what about distributivity condition satisfied by toposes but not by quasitoposes????? or something.... ???....

??so what _about_ "zariski quasitopos of a smfcca" ??? ... and so forth...

is the category of modules of a ring object in a quasitopos generally a finitely cocomplete algebroid but not an abelian category?? (??relevance for smooth spaces?? ...?? ??also consider examples like simplicial complexes... ???...)

??so what about quasi-locales???? (or something...)

??so what about "the logic of quasitoposes" ??? might it be something about ... ???some one particular "modal operator" or something???? something about comparable pair of grothendieck topologies... ??something about "ghost points" ... (??relationship to "voodoo mathematics" ??...) ??... ??is it really just "split-level" like this?? ??if so then how do you recover an injective geometric morphism of toposes from a quasitopos?? ... or something... ???... ???what _about_ relationship to enrichment in categories ct in groupoids?? ... and so forth...

??so what _about_ coherent sheaves over the (zariski) line, separated for the topology which removes the origin ?? ... and so forth...

??also simply sheaves over it, separated for that topology ...

?now realizing that a lot of my vague memories about "quasitopos" are tangled together with idea of "concrete quasitopos" ...

??locale as quasitopos where all points are ghost points ??? ... or something??

something about "distributive" aspect of topos vs of locale ... and so forth... ??...

??free quasitopos on ...?? ... ???... and so forth...

??"quasi-geometric theory" ... ???...

??quasi-topos as mix of topos and locale?? or something?? ...