?? hmmm .... idea that toric case of tannakian philosophy is about extra toric convolution tensor product ... ??? perhaps valid to some extent, but ... ?? don't forget _un_combined doctrine .... pure TAG doctrine .... just symmetric monoidal cocomplete category .... cartesian product not in TAG doctrine, so .... ??? no toric convolution .... ??? .... ??? so ... ???? really does seem to be true that TAG + niceness associated with "flatness" and "accidental topos" leads towards some genuine (?? ...) sort of "toric"-ness ??? .... "toric convolution" ?? .... ??? pushing envelope here with stackiness ??? ... ????

??? trying to adapt thoughts here to apply in other cases .... ???? AG instead of TAG .... ?????

??bit about tensor product on accidental topos as .... ???? how did it go ???? ..... ??? extra left adjoint of essential geometric morphism .... ???? adapting to AG case vs adapting to "TAG case from toric convolution viewpoint" ... ??? ....

????? accidental quasitopos ????? ..... ???? still analog of "toric convolution" .... ?????? ...... ???? ..... ....

??? recovering quasitopos from coalgebras in it ???? ...... ???? ....

?? hmmm .... ?? back when we were first (?? ...) noticing the existence of nice (?? ...) non-abelian cocomplete algebroids .... ???? and considering free monoidal and free symmetric monoidal enhancements of such .... ?? had feeling about .... seemingly "minor" variation on "hopf alg" / "bialg" / "algebraic group / monoid" that nevertheless seemed also impressively weird ... ?? ...

??? "filtered ..." .... ???? ....

... walking epi .... ???? .....