?? so let's try cooking up an example of day convolution where the (binary...) tensor product doesn't have a "second right adjoint" ... ???which should be pretty easy, if i'm thinking about this the right way... ???just need to pick a "generic" (...) example ?? ... pro-monoidal rather than genuinely monoidal ....

???also... got into discussion with todd about ideal class groups and dimensional categories and so forth ... ??follow up on this ... ??blow-up and so forth ... ??but also ... ???toric ideal class group ??? .... ??? .... ???? .... kummer .... ??? .... ??? gunnarsen ???? ...... rng ... ??? ....

???? "checkerboard corner" ... "downward decorrelation" ... "localization" .... "ramification" .... ????.... idempotent vs invertible ... ???? ..... checkerboard edge ... ???..... ????? ...... ?????? ........... ???? filtered colimits vs ... ?????? .... ????? .....