hmm... ??with this "existence and equality predicates" business, seems like... ???the "actual universe" is a "subquotient" ofthe "nominal universe" ?? or something ??? ??does that make any sense ???....

??well with a general map, neither domain nor co-domain accounts for all the stuff, right?? ... both contribute some ... ??? or something ???...

hmmm...

??what about something... ??functor from boolean algebra to subquotients of nominal universe ... ??or something?? ...??...

??what about some stuff here reminding us of ... ??some semi-recent stuff about zariski topology for boolean ring ?? ... or something ... ??where was that?? ... ??notebook358, or something ??... (maybe right around p 207, which is where i just happened to open to ... ??..) ... mixed in with some stuff that didn't make that much sense, i think, but .... ??... (??something about ... ???apparently incorrect idea that i had about ... ??some sort of "stalk-wise" version of booleanness of a heyting algebra... ??? or something .... ????....) ... hmm, but stuff around p 207 does seem surprisingly close to stuff we're trying now ... or something ... then weird maybe interesting stuff before that ... ???...

??something about ....???promoting an idempotent to invertible as promoting it to 1 ... ??or something ???....


??open sets of a sober space form _what_ kind of frame ??? ...

??something about ultrametric spaces ... ??? or something??? ...