??so is the topos of set-valued functors on the fan category of a toric variety v essentially just the topos of toric non-quasicoherent sheaves over v ??? ... have we ever thought this before ?? ... ??? ....

how good (??) of a TAG theory (??...) does this (?...) topos itself qualify as ?? .... ???? ....

??in particular do we (??obviously) get that (...) same compatibility (??) relation between the topos and TAG structures ?? ...