?? so consider ... ??? ag morphism from projective line to "1" ... ?? ....

_set_ -> tqs(p^1) .... ???? "constant" ... ??? ....

[x X n_-] -> [x X z] <- [x X n_+]

?? doesn't preserve terminal object .... ???? .....

?? sense in which process "s |-> sXm" from _set_ to _set_^m (m single-object smc ...) induces process "v |-> v#k[m]" from _k-module_ to [k[m],_k-module_] .... ???? .....

?? some sort of 2-fr f : _cat_ -> _k-algebroid_ .... ??? .... ??? k-module objects in category c .... ???? niceness requirement on cat and / or k-algebroid here ..... ???? .........



?? applying hypothetical f to 1-cell given by "s |-> sXm" ..... ???? ....

?? maybe try case where 1-cell here is a bi-presheaf ..... ????? ..... ?? f simply takes free k-bimodule on bi-presheaf .... ???? ...... ??? but can we adapt this to the case where bimodules are replaced by general cocontinuous functors ?? .... ???? .....

?? trying to use eilenberg-moore category ??? .... ??? canonical presentation ?? ... ??? ....

?? how tensor product ("#") gets along with presentations .... ??? ....

???? simply .... ???? considering how the _right_ adjoint acts on k-module objects, and then taking the left adjoint of that .... ?? ... ?? perhaps also "more explicitly" (?? ...) describable along lines suggested above .... ??? ....

?? global sections ..... ??? ....

?? how automatic _is_ it that there's a good tensor product of k-module objects coming from the tensor product of plain objects ?? ... ??? ...

?? consider for example categorified study multiplication here .... ??? .... hmmmm .... ??? k-module objects maybe work nicely in this case ??? ....