??relationship between moore-postnikov-like factorization of functor and that of its adjoint ... ??particularly in connection with ... degenerateness of some of the factors ... ???moore-postnikov-like factorization _of_ adjunctions ...

??seeing something like this in context of... ???reflective subcategories ... inclusion vs reflector ... ??? what sort of "surjectiveness" (??...) property reflector has ... ??? .... ?? "does nothing but universalize some cocones / co-yoneda morphisms ..." .... ?????relationship to "localization" / "invertiblization" ... ?? ??hmmm... ?? "conservative" orthogonal complement .... ??? "cocontinuous functor that reflects universal co-yoneda morphisms" ... ????....

?? _is_ motivation for "co-yoneda lemma" anything similar to why i've suddenly been thinking about "co-yoneda morphism" ?? ... ??namely as more "invariant" ("eliminate the middleman") version of "cocone" ?? ....

?? "universally universalize all of the co-yoneda morphisms that are universalized by cocontinuous functor f" ... ????..... ???as giving "reflector" ... ????left adjoint to inclusion of ... ???

???so _is_ this concept essentially just what people mean by "reflects colimits" ??? .... ??and how many puns on "reflect" are there here?? ...

(??several perhaps ??? ?? "reflect isomorphisms" ... ???... well perhaps that one's not really a pun, but ...

??["reflects colimits" as implying "reflects isomorphisms"] as aspect of what was striking me as weird last night ... ??? ....)

(??? monicness of co-yoneda morphisms .... ????what _is_ going on there ??? .... topos ...

???hmmm... i just tried looking at representabilization of presheaves on a finite toset, aka "n-stage trees" ... ??seems like the universal co-yoneda morphisms are all epi .... ?????is that maybe just an accident in this case ??? ... ???all reflective subcategories being distributive lattices ... ???.... ?? .... well wait, seems like they're not quite _all_ surjective ... ??? representabilization of empty presheaf ??? ....)

???colimit diagram schemes that are finitely complete ?? ... ???....


full-and-faithful right adjoint ... colimit-reflecting left adjoint ... ???? no wait, i was trying to match things up but i think maybe i got the wrong ones matched up ... but anyway, i think that setting up a correspondence like this, but correctly, is part of what we'd really like to do ...