For some reason, I found myself minded to spend a bit of time tidying up the pages on posets and Galois connections that I was working on some weeks ago. They have the form of the first two chapters of something longer, something that may or may not get written — but these pages should have some stand-alone interest. Here’s the new version. As always, comments gratefully received. (Thanks so far to Tim Button and Luca Incurvati — and in particular to Nathan Bowler who gave a talk in which he explained the basic idea of syntax/semantics as a Galois connection, which inspired me to write these pages.)
[Later: Monday 30th June] And that link is now to a better version, with some paragraphs about quantifiers as adjunctions, and some superfluous material removed for later use.
Excellent! I’ve been presenting some stuff from Dunn’s book on gaggles to some people around Pittsburgh. I have been using the earlier version of the handout to illustrate a concrete instance of Galois connections, as concrete as classes of models and of sentences are, and it has been extremely helpful.