?? categorified multiplication and categorified comultiplication for structure types ... ???

"from structure type on pairs of sets, get structure type on sets" ... ??? multiplication .... ??? ... ?? special case where structure type on pairs of sets involves "no correlation" between the two sets .... ???? ....

"from structure type on sets, get structure type on pairs of sets" ... ??? comultiplication .... ????? "new structure on (a,b) as old structure on a+b" .... ??? ....

??? structure type t tw .... ??? nice morphism from comult(t) to ... ???? ..... "no correlation" structure type ........ ???? .....

?? clear up .... ???? .....

?? morphism from comult(t) to t#t ???? ..... ?????? ..... ?????? ......