hi. i think that we said that we'd try meeting tomorrow, sunday that is. i just want to try to mention here some topics that i hope we get to talk about. actually, there are so many topics that i want to talk about, that there's little hope that we'll actually be able to talk about all of them tomorrow (even if you don't have topics of your own to bring up as well, which seems unlikely).
among the topics that i want to talk about are both:
1:
ways of resolving some of the technical difficulties(?? os??? asf os...) problems that we've been trying to solve so far, such as how to prove some improved version of your theorem about the quasicoherent sheaves over P^n as forming a specific (cocomplete...???os...) ag theory. and also, dealing with questions that you (??and me?? ??os...) have raised in connection with this... os... asf os...
but then also:
2:
topics that i'm very interested in but which we haven't gotten around to talking about yet because of focusing up till now on #1 above... (and also becaause of my general slowness, asf ...????) ... topics which are somewhat more "conceptual" and less "technical" (os...) ... ????sa interesting questions that raise themselves once you get beyond the technical difficulties... ??either by actually resolving those technical difficulties, or by optimistic thinking... ??os... ??sa fe things that alex and i have worked on, that you asked about at one point, if i remember correctly...
???and actually the above division into #1 and #2 is somewhat artificial, there being lots of overlap... some of the alleged "technical" questions being actually conceptually very interesting, when you think about them the right way... ??...anyway, i'll proceed to try to list some items from #1 and/or from #2, hopefully making clear which of #1 and/or #2 i'm placing it in... ??os...
#1
???finitely cocomplete vs cocomplete ....
#2
???lots of examples of ag theories ... working both from "syntactic presentation" end (??maybe really "semantic" end??? ) and "syntactic category" end ... ???os???
epimorphism from 1 to 1+1
maps a,b : 1 -> 1 which are each other's cokernel ...
n-dimensional object (??variations???)
dualizable object (adjoint pair of objects)
object
epimorphism
free ag theory on a finitely cocomplete algebroid ...
string of good embeddings starting with 0, with each cokernel invertible...
???something about ag theory of n-tuple of line bundles equipped with (for example) lie alg structure... and so forth ...
n-dimensional lie algebra object ...
???something about cuboquadratic algebra ... ???...
?????sa doctrines.... ????
??something about big zariski topos....
finitely cocomplete algebroid ...???
????something about cohomology... derived categories... and so forth ... ???....
???something about "renormalization" and so forth... filtered... associated graded ... and so forth... normal bundle... ???...
martin mentioned something about "algebraic theories" today... so i think that i should try incorporating this into the discussion... something about "doctrines" ...
blending together various viewpoints... algebraic theory as parallel to ag theory ... and so forth ... ??
??also something about "universal property as tool for reducing abstraction level" ... and so forth... ??...
???i guess that this message came out even more disorganized than i expected... so maybe it won't be too readable for you, but maybe i can at least use it as a reminder for myself about some topics that i might like to eventually bring up...
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