?? issue of ... ?? more 2-morphisms between accidental geometric morphisms than i was expecting ... consider affine case for example ... ?? things to think about here, but main idea seems to be that ... ?? am mainly interested in "symmetric semi-monoidal geometric morphisms" here .... ??? ....

?? annoying how this complication bumps into the complication of mere semi-monoidalness vs actual monoidalness ... ?? ...

??? "translation vector space" functor of affine space ... ?? relevant here ??? .... ?? as retraction of ... ???? .....

?? theme of "modules of commutative rings vs representations of groups" here (...) ??? .... ???? ..... (?? ... contrasting flavors of tensor products ... ?? ...)

??? "unstackiness" condition on symmetric semi-monoidal grothendieck topos ... ???

?? hmmm, this "more 2-morphisms between accidental geometric morphisms than i was expecting" issue .... ?? hoping now that it's really more or less just same as issue of what kind of structure correspondences have ... co(???sesqui ???)-/monoidal wrt "ordinary" tensor product, vs ... ???? ... ??? .... ... ??? getting toric convolution involved here ?? ... and / or abelian variety cousin of it ....?? ...

?? idea that has bugged me sometimes .... ?? situation where suddenly revealed cryptomorphism links previously inscrutable concept x to .... about equally inscrutable concept y ... so if you were hoping to reduce complex to simple in most strsightforward way then that's not what's happening here ... ?? but then, arguably, the cryptomorphism can still be highly valuable ... ?? ...

?? hero in disguise/hiding vs in disarray/disgrace ... ?? ambiguity between these ... ??? ....

destry .... ??? hamlet ... superman ... zorro ... pimpernel ... hermes/zeus ... ??? ... kenobi ...

?? ray ... ?? reappearance of hero ?? .... ?? particular example on tip of my tongue .... ??? .... resurrection / regrowth .... ??? ...