?? so .... ?? contravariant functoriality of homming ringoid (?? ...) into ringoid of all ab gps ... ???? ... ?? also preservation of tensor product of ringoids ???? ... ???? .... ?? allowing [x,_ab gp_] to become model of p^op (?? ...) where x is a model of prop p ... ??? .....

?? but maybe also some covariant functoriality ?? ... ?? and looking at the codomain slot as variable as well .... sesquivariance .... ???? .... ?? p^op # q ?? ... ??? ....

?? idea maybe we're suggesting module cat of comm ring is more saliently co-monoidal than monoidal ??? ..... ??? weird from "doctrine" viewpoint ?? ... ???? .... ????? ....

[note added several days later : hmm, i was going to add a note here remarking how screwed up this was ... ?? but maybe it's only about as screwed up as we already realized it was at the time ... ?? ...]