??todd mentions something about ... ???... some functor (??something about "inclusion of accidental topos of smaller affine toric open into larger" ... or something ...) being a geometric morphism of toposes because of something about some action of some commutative monoid being flat, or something ... ???which makes me wonder about something about "flatness of localization" and maybe vaguely related stuff ... ??and so forth ...

??something about ... diaconescu's theorem as about model of certain geometric theory ... ??something about construeing that model as a geometric morphism ... ??so is that part of what todd was saying, and/or does it fit with what todd was saying ?? ...

?? given flat action x of commutative monoid m ... ??construe this as model of theory of "m-torsor" ... or something ... ???... ??so something about geometric morphism from geometrically terminal topos to

???hmm, something about... ???model here as thing that you tensor with to perform geometric morphism .... ??hmm, something about "building blocks co-presheaf" and bit about simplicial sets as classifying topos for "interval object" or something... and so forth ... something about "flat building-blocks co-presheaf" ... ?? and so forth ... ??_is_ this really all fitting together ??? ...

???something about "model" and "realization" ... ???something about "geometric realization of simplicial set" (for example) as ... how "formula" (= simplicial set ...) is realized in model (= flat building-block co-presheaf) ...

??"geometric realization process" associated to flat building-blocks co-presheaf as "the realization" (of "the theory" ... ??...) more or less synonymous with "the model" associated with the flat building-blocks co-presheaf ...

??so something about walking 1-simplex simplicial set as "main formula" of the theory... "generator" ... ???something about "carrier" ... ???or something... ??? ... and so forth ... "the interval object" itself ... ???any other simplicial set as built up by limits and colimits from (mostly ... ??...) just walking 1-simplex... some fuzziness here, but ... ??...

??so what about something interactions between various doctrines here... ??... diaconescu's theorem in doctrine of geometric theories... but with perhaps even more fundamental (??or something??...) analog in doctrine of abelian categories ... ??but with doctrine of ag theories perhaps more relvant ... ??but then with doctrine of tag theories perhaps even more relevant ... ???and so forth ??? ...