?? so we're still trying to straighten out the correspondence between "toric" operations on a toric variety and (so-called ...) "geometric" operations on its accidental topos, with the totally defined among the former corresponding to the essential among the latter ... ?? ...

?? so the toric variety has its binary multiplication operation, totally defined (?? precisely ??) in the affine case ... ?? and also its nullary multiplication operation, always totally defined ... ??? and it has its co-binary diagonal operation, and its co-nullary "total projection" operation ... ?? except that the latter is perhaps not actually toric in the non-affine case ???? .... ?? not quite sure yet ... ?? might depend on haggling over definition of "toric" here ?? ... ?? relationship to issue of "preservation of basicness of toric open subsets by inverse image of toric map" ??? ... anyway, the latter two seem to be totally defined when they exist torically ... ??? ...

anyway, on the other side of the correspondence, we seem (?? with the help of some somewhat wild guesses ...) to have ... ??? the co-binary diagonal operation on the accidental topos, essential precisely in the affine case ... ??? which it would probably be nice if this is strongly linked with the total distributivity of the topos ... ??? ...

?? and we also have the co-nullary total projection operation on the topos ... ?? always essential ???? ...

?? and the binary "multiplication" (?? ...) operation on the topos ...

?? and what about nullary "multiplication" ???? ..... ???? apparently missing in filteredly cocomplete picture ... ??? ...

??? still lots of confusion here .... ???? ....

?? testing above guesses in affine case should be somewhat good consistency check here ?? ...