x pro-monoidal category ...

x1 # x2 as presheaf on x ... formal colimit of x-objects ... so ... element of presheaf x1 # x2 ... over x3, say ... as x3 -> x1 # x2 ...

???so ... ???binary and nullary operations in concrete operad of yoneda image objects in opposite monoidal category .... ??? ....

?? "associativity" ... ???..... ???isomorphism of pre-sheaves (?? of 4 variables ... ?? 1 of them of different variance ?? ...) between certain "tensor product" presheaves ??? ... ???more concretely ... ???.....

a#b -> c .... c#d -> e .... ????

??? getting quadratic operad from arbitrary operad at expense of introducing compound types ??? .... ??? maybe either via getting pro-monoidal category from operad, or just sort of directly ... ???....

??possibility of ... ??? 3(?...)-codiscrete simplicial "nerve" of pro-monoidal category and/or of quadratic operad? ... ??with "something extra" amounting to mere property in both cases ?? ... ???reflective in quadratic operad case ??? ...

??possibility of just "facial" nerve ??? ... ??maybe in "quadratic operad" case ?? .... ???? ....

??in "untyped" case, just set of 2-cells tw 4-ary relation ("form a 3-cell") ?? ...

?? homotopy type of such simplicial set ... ??? ... ???in "accidental topos" case ??? ....