[transcribed from paper ... semi-recent ... ?? couple of weeks ago ?? ...]

[m,_set_]__cat_ ?? co-[comm monoid] ?? ... m -> mXm -> _set_X_set_ -> _set_ .... ?? cartesian ...

[comonoid,monoid] ... ???

?? functoriality we've been trying to exploit as not quite right one(s ?? ...) ... ??? (?? and we _are_ jumping into idea about "stably co-(??? note added later : ?? thinko/typo here ??? ... ???) again ... ?? ... geometric morphsm being homomorphism here ... ??? ...) ... ???? "functions" vs "measures" ..... ???? adjunction vs monad ??? .... z vs z/2 ??? .... ??? but just -1,0,1 as reliable ?? ... ??? ... ?? "co-arity" operations as very unavoidably involving "X going to #" ?? ... ?? ...

?? "haar measure" ... ??? "serre duality" ....

?? "kronecker delta" (?? extent of functoriality thereof ... ?? ...) ... "frobenius reciprocity" ... ??? ....

?? specialness of omultiplication |-> specialness of multiplication ... ???? .... ?? diagonal .... cartesian product .... ???? ?? funny level slips ??? ... ??? riding ?? ...

?? "projection formula" ??? ... ???

?? prop for [[?? indecipherable ??] plus bialg] ... ??? ...

?? sets and relations inducing vsps and operators ... ?? and / or categorified ... ?? .... ?? hecke ??? ... ??? categorified bialgebra ... ???? cartesian bicat ... ??? ....