?? universal property of [category of structure types] as "toric category" ... ??? ...

??? relationship between operational structure on object wrt operation o (?? microcosmic level shift here ?? ...) and ... ??? co-operational structure wrt (left ?? ...) adjoint operation o' ?? ... ???? .... ???? .... co-monoidal category ... microcosm ... level slips/shifts ... ??? ..... cartesian ..... 2-sided .... ??? .... ??? ...

?? "co-x object" vs "co-object" ... ??? ....

l(x) -> y .... x -> r(y) ....

??? x#x .... ??? ....

f(x) <-> x#x .... ??? ....

x <-> g(x#x) ..... ???? .....

l(a) -> b#c ....

a -> r(b#c)

?? r categorified multiplication, l categorified comultiplication .... ??? .... ??? ....

"operad" .... ?? "co-operad" ... ???? .... ???? ....

?? diagonal and cartesian product here .... ??? .... .... hmmmm ..... ???? ... ??? model of operad in (_set_^op,X) ... and / or in (_set_,+) .... ???? .... ???? .... ??? "component" of operation .... ??? ....