?? if tensor product and toric convolution correspond respectively to "diagonal" and "multiplication", then ... ?? should / do they act just like those act, namely in some sort of "(categorified ... ?? ...) bialgebra" way ???? .... ???? .... ??? index raising/lowering games here ???? ..... ???? ..... ?? "lax interchange" .... ???? .....

?? egger ??? ... ??? micricosm principle ?? .... ??? ...


??? "symmetric semi-monoidal topos" ... ??? semi-_co-_monoidal cocomplete category ??? .... ??? ..... ??? "semi-bi-monoidal ..." ??? .... ???? ..... ???? ....

?? ... adjoints .... ??? .... theory (?? of some doctrine, o maybeof something more general .... ??? ....) formed by some operations together with adjoints of them .... ???? .... ???? ....