???no unit object for intersection of basic affine opens ??? ...??? ...

??? "pro-unital" ??? .... ????...

???confusion ... day convolution wrt monoidal (or more generally pro-monoidal...) structure ... ???vs ... ??geometric morphism induced by monoid product ... ??? ... ??"essential" ??? .....

??day convolution as "extra left adjoint" of essential geometric tensor product ... ??well, in the case where there's an actual tensor product rather than just "pro-" such ... ??? ....

???doctrine where an environment is .... ???a topos t, equipped with (??the extra left-adjoint part of) an "essential tensor product" ... ???? .... ????....

(??still confusion about "theory has moduli stack over site given by ..." vs "environment has ... " .... ??? ... ????"formula has solution presheaf over site given by models" ... ???thing that "has" solution presheaf as same kind of thing occurring as object in site ... ???? .... ???? .... ...... ?????? ........ ??"theory" and "environment" as similar ...... ???????.....)