?? free AG theory on TAG theory t1 -> AG theory t2

=?=

t1 -> underlying TAG theory of t2

??? .... ???....


???underlying TAG theory of AG theory of modules of comm ring k ... vs ....

TAG theory of actions of mult monoid of k .... ???? ....

???some confusion here ?????? ........

???????????????? .....

??? affine variety case ???? ..... ???? ...

??right adjoint process of taking underlying mult monoid, followed by ... ????is taking actions a left adjoint process ?? ... ??? .... ???

???............


??? 2 very different ways to get from a toric variety v and a commutative ring r to a set of something sort-of like "points of v over r" ... ??? .... via taking mult monoid of r, vs via taking underlying TAG theory of AG theory of (syntactically) r-modules ... ??? .... ??with some further confusion about possible ways in which maybe this distinction gets somehow blurred in "affine" case ??? ... ???? .... ????....

???check certain e-mail i was writing to todd to see to what extent i might have gotten this stuff screwed up there ... ??e-mail about moduli stack of elliptic curves as toric stack ... ??? .....

???getting pre-stack over _comm ring_ directly from pre-stack over _comm monoid_ ... ????....... ???? .....

???maybe distinction really does vanish in "affine" case ??? ??then what about "close to affine" ??? ... ??? ....

???comparison functors between ... ??actions of mult monoid of comm ring k, and k-modules ??? .... ?? ... ??? and what doctrine such comparison functors might qualify as theory morphisms wrt ?? .... ???? ....

??underlying [mult monoid(k)]-set of k-module ... free k-module on [mult monoid(k)]-set ... ??? ....