?? homotopy type of accidental topos of toric variety .... ??? ... ???affine and non-affine cases .... ????? ..... ??how TAG structure relates to it ??? .....

co-/homology groups of this homotopy type ... ?? as relating to abelian category of abelian group objects in the topos ... ??? .... which is of course (we think ... more or less ...) the quasicoherent sheaves over the toric variety ....

?? this direction of thought ... and/or perhaps other vague thoughts vaguely related ... or at least impinging here ... ?? ... ??? as tending to make it more obvious how likely that all this stuff is already well known in some form somewhere ...

????vague ideas ... old ideas that never really managed to get to work ... ideal class group ... homotopy type / groups of geometric realization of monoid .... non-unique factorization ... octahedron /generalized diamond ... ?? .... ??? ....

?? ... thomason ... ??? ...