Friday, April 1, 2011

??hmm, have i been falling into a slight glitch here??? ... something like ... ???given a filteredly cocomplete category, you want to somewhat systematically look for a topos with it as classical model category... or something like that ... so... ??that means that the site category should actually be the opposite filteredly __complete category ... ??is this really correct?? ...seems like it shoul be ... ??does this maybe help to straighten out any (??especially "variance" ...) confusions that we were having ?? ... ??something about "frankenstein doctrine" and so forth ??... ??something about "pre-sheaf vs co-presheaf" ??? .... ???and so forth ??....

??actually i'm pretty confused right now; not sure which (...) way it should go ... ??something about idea that ... ???in formulating a grothendieck topology, doesn't it make more sense to use _colimits_ in the site category ???? .... ???or something??? ....

... really try to straighten this out ... ??...

??well, i'm trying to straighten it out but getting _really_ confused ... ??something about ... ??seemingly very opposite (or worse...) ideas about ... ???relationship between open set and sheaf (or something ... ???) associated to it ... ???? ...... ????????? .....

??something about sheaves and weak limits and so forth ... ??? ....

???hmm, so what about the possibility that the main big confusion here is that rather than considering sheaves for a grothendieck topology here, what we really want here is something about ... ???filtered _co_-limit-preserving set-valued functors .... ????or something ???? ..... and so forth .... ????......

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