?? so given geometric morphism between accidental toposes ... ?? we think that we can factor this into .... ???? well, thinking in toric picture ... ??? ... "first", narrow domain to dense toric open ... ??? meaning that we've got a geometric morphism that's also a tag morphism .... with the "algebraic left adjoints" coinciding .... ??

??? surjection-injection factorization of geometric morphism between accidental toposes .... ??? ...

?? injecction part as corresponding to narrowing domain to dense toric open .... ??

?? surjectionpart as .... ???? .....

?? tag morphism where algebraic left adjoint has left adjoint ... ?? vs ag morphism where that happens ... ??? vs g morphism where it happens .... ???? ..... ??? geometric interpretations ??? .... ???? .....

?? "enough global functions" ???? ..... ????? .....

?? ag morphism ... geometrically from p^1 to 1 ... ?? algebraically taking vector space to tensor by it of unit quasioherent sheaf .... ?? right adjoint given by ???.... global sections .... ????

??? non-projectiveness of unit object ..... ????? ..... ??? homming from it as not preserving cokernels ????? ?? epi defined as having zero cokernel ??? ... ?? not preserving epis ... ????.....

??? homming from unit object as always (??) right adjoint ... ?? quotient of whether it in turn has right adjoint ????? ....

??? right adjoint to "underlying vector space of module" .... ???? "histories" flavor ??? ....

?? bi-module formulation here ???? .... ??? adjoint bi-module .... ???? ..... ???? .....

?? "topos-geometric morphism fitting together with tag-geometric morphism in way that happens with arbitrary totally-defined toric map between affine toric varieties" ...

?? vs "... in way that happens with arbitrary narrowing of domain to dense toric open" .... ?? ...

??? adjunction / monad /co-monad associated with injective / surjective topos-geometric morphism .... ???? .....

?? somewhere here seemed like i was anticipating ag / tag morphism with "algebraic left adjoint" having extra left adjoint, but then instead seemed to run into its right adjoint having extra right adjoint ..... ???? .... ?????? ......