?? so does tensoring with a non-trivial line bundle give an endo-[geometric morphism] of the accidental topos of the projective line, for exsmple ??? .... ??? or auto, maybe ... ?? ...

?? hmmm .... ??? how could it possibly not ?? ... (?? also ... consider non-toric analog .... ??? ....) ... ?? so then ... ?? how complicated is this going to make it giving a nice explicit description (in paper ...) of geometric morphisms in general here ???? ..... ???? .....

?? was going to suggest idea of using "categorified moore-penrose inverse" (somehow ...) here, but .... ?? confusion ??? ...

?? by the way, to what extent have we thought about how toric automorphism group of projective n-space fits in its ordinary (??) automorphism group ?? ... ???? ....

?? kock-zoeberlein .... ???? ....

?? endomorphism vs morphism here ... ???? .....

?? op(?? or sesqui???)-/lax vs strong monoidal structure here .... ???? ...... ... ??? ....

?? idea of getting toric map from surjective (?? ...) geometric morphism here .... ?? how screwed up is that now ??? ...... ??? maybe tensoring with any line bundle gives the identity ???? ..... ??? hmmm, and maybe treating injective and surjective separately makes it easier to keep various sorts of complications (non-trivial line bundle vs sub(?? in _some_ sense .... ??? localization ... ??? ...)-bundle of trivial line bundle .... ??? ...) from interacting with each other too horribly .... ??? but where are we suggesting that the twisting line bundle should live ??? .... i was going to suggest 3 possibilities domain, image, co-domain .... ?? but maybe there's some motivated way to choose one of these as the right one by thinking in terms of pullback ..... ??? so, very naively, seems to me like that would suggest taking line bundle to live on domain of toric map ... ?? on principle that if it lives on one of the other two it can be pulled back to the domain ..... ????? .....

?? hmm, maybe key example is .... geometric morphism from geometrically terminal topos (?? as accidental topos of terminal toric variety ... ??? ...) to accidental topos .... ???? ....