so... another stab at "textbook" description of "isbell conjugation" ...

??so it looks like they're saying that there's a certain functor from small category c to [c,_set_]^op .... ???that then gets left (or something...) kan extended to give left adjoint functor from [c^op,_set] to [c,_set_]^op ... ??or something ...

so... hmm... that's equivalent to from c^op to [c,_set_] ... which there certainly is the obvious choice of such ...

"geometrically realize presheafs as "opposite co-presheafs", using as realization scheme certain hopefully obvious version of yoneda embedding ..." ???or something ...

??consider for example c = _simplex_ ...

??or maybe just 0d and 1d simplexes .... ???....

???something about "family of bi-pointed sets" or something ???

???so ... ???we want to realize the 0-simplex and 1-simplex as families of bi-pointed sets in a certain way...

???the 1-simplex as ... ??singleton family whose set has 3 elements ???

???0-simplex as singleton family whose set is singleton??... ??...

???not quite making sense yet ??? ..... ??maybe rather 0-simplex as singleton family whose set is doubleton ... seems to make sense ...

??something about geometric realization here as involving "co-glueing" rather than "glueing" of co-presheaves ??? or something ??...

??hmm, so what about something about ... ??? ??getting co-presheaf by homming given presheaf into each representable presheaf in turn ... ??and so forth ???... ??something about "bipartite" version ... "getting y-presheaf by homming given
x-presheaf into each of [y^op]-presheaf of x-presheaves" ... ???or something???

??something about ... ???homming variable thing into constant thing ... as turning colimits into limits ... ???and so forth ... ???.... ???something about stuff about ... weak limit ... and so forth ... ???....

???so what about something about?? ... whether isbell conjugation is "self-conjugate", ifykwim ... ???... ??something about whether both of the adjoints can be viewed as "spectrum", or something ??? .... and so forth ...

also ... ???what about something about "algebraic geometry" examples, and especially categorified such ...?? ... ??something about ... doctrine ... with family of favorite environments ... ????something about extent to which the two conceptual "parts" can be freely transposed in the "bipartite" case ... ????....

???something about ... ??"pairing" between commutative rings and ag theories, for example ... ??...

???something about... ???given a "pairing", using formal colimits on one side and actual colimits on the other side, vs using formal colimits on both sides ... ???or something ??? .... and so forth ... ??? (??something about trying to view former as special case of latter ... ???and so forth ...?? ...) ??what _about_ "variance twists" here, and so forth ??? ....

???something about ... ??naive "restricted yoneda embedding" / "spectrum pre-[sheaf/stack]" idea ... ???can be applied to presheaves, for example ... ???resticting along the yoneda embedding, os??? .... ???hmmm, so what _about_ all this "isbell" stuff as to do with some case of "yoneda embedding restricted along yoneda embedding" , or something ???... x-presheaves contravariantly yoneda-embed into [x-presheaves]^op-presheaves ... which can then be restricted along the yoneda embedding from x^op to x-presheaves, to give x^op-presheaves ... ???meanwhile maybe there's a sort of opposite way of "restricting the yoneda embedding along the yoneda embedding", just with ops in different places, that just gives the identity functor ??? .... ???if so then _why_, exactly ???.... ??hmmm, could yoneda lemma be construed as sayign exactly that this is the idnetity functor ??? ...???or something ??? ...


??so i'm sort of guessing that people are thinking of co-presheaves on the category of (maybe "finitary" or something...) affine schemes as sort of "generalized commutative rings", and then homming them into actual commutative rings to get presheaves on the category of affine schemes ... well, not sure that i said that exactly right yet, but in any case i'm not too impressed so far ... are any really "interesting" presheaves supposed to arise this way?? .. and so forth ... ???...