??something about ... ???... accidental topos of toric variety ... ??something about "toric quasicoherent sheaf" ... ??taking concept of "quasicoherent" here slightly seriously ... ???... ??something about sheaf topos over "toric small zariski topos" ... equipped with "structure sheaf" commutative monoid object ... actions of this commutative monoid ... forming a topos... ???but with day convolution more relevant than cartesian product... ?? and with quasicoherence constraint ... ???? and so forth .... ???

??something about relationship to face poset of fan, or something??? .... ???...

??but then what about relationship to "_right_" way of using topos theory here ??? ...