?? [idea that "restriction along diagonal" is cocontinuous extension of cartesian product of presheaves] as fitting with [idea about decategorified analog of cartesian product of presheaves] ???? ..... ??? though in these contexts maybe morally better to think of "set-valued functors" than "presheaves" .... ???? ......

?? so then left adjoint of this restriction process as "geometric realization of presheaves as bi-presheaves, taking basic figure to "its square"" .... ???? .... ?? which, again, seems to be fitting with .... ???? naive expectation about categorified comultiplication compatible with tensor product (?? by which i seem to mean "day convolution" here ... ??? ....) as categorified multiplication .... ???? ....

??? so go ahead and try investigating "non-affine" case here ... ??? ....

?? idea of ... ??? question of whether diagonal is automatically essential ... ??? try to identify diagonal geometric morphism and/or its extra left adjoint as part of "covariant algebraic structure on _set_" ... ???? but seems very degenerate from this point of view .... ?????? ...... diagonal of terminal object as very degenerate .... ???? ..... identity functor ... so yeah it's left adjoint exists too, but ... ??? .... ?? ...

?? non-toric analog of "object as function wrt topos structure, measure wrt categorified bialgebra structure" ??? .... ??? maybe makes some sense ??? .... ?? quasicoherent as function wrt abelian category structure, measure wrt symetric monoidal cocomplete algebroid structure ????? ..... ????? ...... ?? is this telling us about some sort of "exact pullback (?? ...)" here ???? ... ?? .... ???? confusion ... ??? .... ??? further confusion ..... ???? sense ("moduli stack" ... ???? ...) in which quasicoherent sheaves are definitely (?? ...) supposed to be like functions wrt smcca structure .... ??? ..... ???? ... ??? "intensive vs extensive" ... ??? as very confusing / messed up / complicated when "spectrum" carries further algebraic (?? ...) structure ...