Subject: categories: Re: Laws

From: "George Janelidze" <[email-masked]>
Date: Thu, 10 Aug 2006 02:19:51 +0200

Dear All,

What Tom says now, and what Bill calls a simple answer referring to Michel
Hebert, also suggests to mention

[H. Andréka and I. Németi, Los lemma holds in every category, Stud. Sci.
Math. Hung. 13, 1978, 361-376]

(although a previous paper of the same authors would be needed, I think).
And I am sure many other people also considered many other candidates for
the concept of a "law" producing a suitable Galois connection. And - no
doubt - many such constructions would produce interesting Galois closed
classes.

However, I think "the Universal Algebra of 75 years ago" gave a beautiful
and fundamental example, were the Galois closed classes are fully and
beautifully described (that Galois connection deals with subvarieties of a
fixed variety, with fixed "basic operators" and so there is no problem with
"What is a variety?" of course).

This does not mean that I am trying to argue with Bill: Of course it is true
that Bill's thesis was a great further enlightenment, and of course it is
true that TODAY seeing only those Galois connections and not seeing
adjunctions containing them and much more (also in Galois theory itself!) is
too bad!

George Janelidze