?? arbitrary sym mon cocomplete cat ...

?? or maybe with underlying cocomplete cat good enough so that ab gp objects can be tensored ..... ??????? .....

??? taking cocomplete algebroid of ab gp objects in it .... ??? ....

?? "toric convolution" live here ???? .... ???? ....

?? ag morphism with right adjoint strong monoidal wrt toric convolution ... ??? .... ?? as arising from arbitrary sym mon coocntinuous fr here ??? ... ??? .... ???? .... ???? .....

?? usefulness of actually having good description of left universal property of sym mon cocomplete cat tqs(p^1) (for example ...) for ... ??? trying to figure out what the "good" morphisms are here .... ????? .....

?? sym promonoidal category .... ??? extra structure making it sym mon ... ??? ... ?? "day convolution" wrt actual tensor product vs wrt pro-tensor .... ??? ... "generalized day convolution" .... ???? ....