?? idea of ... ?? ... i was going to say, ... in thinking in recent days about for example trying to interpret various quasi-["algebraic monoid" ... ??? ...]s as giving categorified (?? symmetric but not necessarily co-symmetric ?? ...) bialgebras whose objects are the quasicoherent sheaves over the underlying scheme (?? ...) of the ["alg monoid" ...] ... ?? that it felt as though we were simply dealing with some sort of "base change(s ?? ...)" between a comm ring of "quantities" and a categorified comm ring of "structures" .... ?? and that we should try to figure out what such relevant base change(s ?? ...) might be, although it also feels like there's something a bit wrong with the idea, in that it's hard to imagine what such base changes might be like .... ?? though it might help if we settled for some sort of zig-zag of base changes instead of a single one ... ??? but then i thought, ... but surely we know in principle "what's really going on" in situations of the sort that we're dealing with here, and should be able to make it much more explicit ... ?? namely, in dealing with the ag doctrine, we know how to interpret regular (?? ...) functions and quasicoherent sheaves side-by-side as structure and stuff resepctively ... ?? and we know a bit about how to relate the pure structure world of schemes to the stuff-y world of stacks ..... ????? .... ?? so then how does all this latter stuff relate to the base change / zig-zag idea ??? ..... ???? ....

??? "cheapo categorification" .... ???? fourier duality .... ???? z/2 (?? and / or z/4 ???? .... ?????) vs z .... ???? ...... ???? ...

(?? "stuff as structures" ... ?? "structure as properties" ????? .... ???? .... ??? known parsing glitches here ??? .... ??? ....)

?? polynomial functions form a comm ring, rational functions form a sheaf of local comm rings ..... ???? ...... ?? field ?? .... ?? division ?? .... ..... ???? .... ?? "being able to divide anywhere the value isn't zero" .... ????? ... ???? .... .... lawvere theory, vs .... ???? ..... affine line vs projective line ... (cockett .... ??? .... did i ever remember to write down idea about .... ?? projective line as classifier not for arbitrary partial functions but for something like "openly-defined" such ??? ....)

?? ask yetter about possibility of some sort of informal seminar ... ???? .... ?? hmmm, warn some people (non-[category-theorists], roughly ?? ...) about "mackey effect" here ??? ....