??lots of different approaches to accidental topos of projective line ... ??or something???...
graded approach...
"globalization" approach....
???sheaves of actions" apporach ??? ... and so forth ...
??relationship between these last two, and so forth??? ...
??filteredly cocomplete category approach ?? ... and so forth ...
??some questions ... ??
???something about .... ????sheaf of monoids ... getting stack of action categories from it ... and so forth ... ???something about "quasicoherent vs non-quasicoherent" here ... and so forth ....
???something about "contrastive element of presheaf" (or _some_thing...) ... and so forth ... case of directed graph ... ???and so forth ... ???but then case of affine toric variety ... ??how to justify those certain elements ( ?? or something?? ) as qualifying as "contrastive" ... ???and so forth ... ????....
??something about issue of to what extent "being torpos" qualifies as "property" of topos ... and so forth ... ???...
something about makkai and pare vs makkai and reyes... and so forth ... ?syntax/semantics duality ... ??... and so forth... ???....
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