?? idea that alleged (?? by that person richard something ?? ... where i heard it, at least ....) absoluteness of all colimit weights over base _cocomplete cat_ is closely linked with perfection (?? ...) of correspondence between left adjoints and bi-quasicoherent sheaves (as "correspondences" in ag context ??? ...) ..... ?? ...

??? and then maybe ... other conspicuous example/s of alleged absoluteness of (?? nearly ?? ...) all (?? higher ... ?? ...) colimit weights .... spectrums, chain complexes (??? issue of dg category vs dg a-infinity category here ??? ..... ??? ....) ... ?? mystical connections here ??? .... ?? (?? quasicoherent ?? ...) sheaf cohomology ... ??? ..... ?? certain level slips ... ?? bit about "derived category as invented in order to get duality to work better" .... (?? that other person's name ??? ...) ???? "duality" here as something about "serre duality" ... ?? and "correspondences" ??? .... ???? .... ???? ....

?? "correspondence" and "motive" .... ???? ..... ?? various sorts of "correspondence" .... ??? .... ?? toric case .... ???? .....

?? combining the 2 (?? ...) examples (of "all colimit weights are absolute" ... ?? ...) in maybe obvious way ?? ... ??? .... "derived-level correspondence" ... ?? .... .... ???? ....

??? case of _cocomplete poset_ ?? .... ???? _cocomplete cat_ : _cocomplete poset_ :: ag correspondence : ??? ....... ??????? .....

?? working out lots more concrete details of _cocomplete cat_ example .... ?? absoluteness adjunction ??? .... ?? .... apply to ag correspondences involving projective line and/or punctured plane ... ??? .... .... ??? ...