?? structure type convolution monoids and comonoids .... certain games with this ... ???

?? "composing and then decomposing as restoring original structure, but not ice versa" .... ???? .... ?? some confusion here ..... ??? "kind of structure that can be decomposed given partition, vs kind that reveals its own partition" .... ????? ..... ?? co-unit as pretty drastic here ????? ..... ?? co-associativity as about equally drastic ??? ..... ????? .... ??? ....

?? non-free structure-type convolution monoid ??? .... ???? ...

??? non-symmetric convolution monoid ..... ???? ..... free symmetric as non-free non-symmetric .... ????? ..... ?? but any non-free symmetric .... ???? ....

??? convolution-monoidal stuff type ???? ...... ????? .... ??? vague feeling of (?? level-slippery) relationship to .... ??? quandle-based knot polynomial ..... ???? ..... hmmmm ...... ?????? ..... ?? action of monoidal structure type on structure type .... ??? ....

?? "zeta-type" as monoidal wrt multiplicative convolution ??? .... ???? .....euler factor ...... ?????? ..... ????? ..... ???? freeness here ???? ..... ?? logarithm of zeta-function ???? .... ?? "euler summand" .... ?????? ......

?? confusion about "euler summand" here .... ??? some sort of 1/(1-x) = 1 + x + ... flavor ??? ..... ????? ..... ?? seems ad hoc .... ??? .... confusion .... ???? ....

?? monoidalness wrt both additive and multiplicative convolution ..... ??? ....