?? some nice easy concrete way to test whether these toposes (the ones associated to non-affine toric varieties) really do lack total distributivity ??? ....

?? relationship between accidental toposes of the toric varieties p^1 and the punctured plane ?? ... i mean in harmony with the projection map from the latter to the former ... ?? ...

?? "generalized day convolution" ... "generalized kan extension" (??or might it _already_ be generalized in that (...) direction ?? ... ??? ...) ... "generalized diaconescu theorem" .... ???? .... ??? "model" picture of alleged essential geometric morphism corresponding to tensor product on accidental topos .... ???? .... ?? then maybe also "model" picture of more general stuff ... ?? "arbitrary topos correspondence" ?? ... ??? ... ?? diaconescu ?? .... ??? ....

?? confusion about ... ???? arbitrary finite limits vs "finite products and equalizers of equivalence relations" ... ??? .... ?? something vs fp presheaves .... ???? ..... ???? .... ?? perhaps not so difficult to work out in some nice way, but i seem to forget a lot of the details at the moment ... ?? ....

?? confusion about whether "vice versa" aspect of "tag correspondence" might be essentially same as "generalized kan extension" (in some sense) ... ???? .... generalized day convolution and generalized kan extension as giving something more special than general tag correspondence ?? ... ??? .... ??? ag / tag confusion here ??? ..... ????? ....

?? hmmm, "generalized day convolution" (?? and maybe then also "generalized kan extension", if that's supposed to be roughly the same idea ... ?? ...) as to do with .... ???? preserving filtered colimits, rather than preserving some kind of limits .... ???? ... ?? so maybe this should resolve that confusion mentioned above ... ??? ....

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