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final algebras



Date: Sun, 27 Nov 88 19:58:52 PST
To: meyer@theory.LCS.MIT.EDU

I inadvertently omitted "ground" when defining "conservative" for
Wand's theorem, which must mean not making new identifications of
*ground* terms, not all terms.  (I had been thinking of calling this
notion /\-conservative, /\ denoting Lambda as per Wand's paper, but
this seemed unesthetic and I dropped the /\.  In retrospect
"ground-conservative" would have been good.)

	From: thatte%cs@ucsd.edu (Satish Thatte)
	There is indeed an optimal augment for any extension and it 
	can be obtained as the *intersection* of all *maximal* base-
	conservative augments in his terminology.

Even easier than I thought.

This (intersection of maximal augments) is easily expressed in
elementary (noncategorical) language.  Is there a reasonable
final-algebra way of expressing the notion of optimal augment?
Intersection (of theories) is a product and the (Galois) connection
between theories and models is contravariant, suggesting that there
should be an initial-algebra way, but what's a reasonable categorical
construction giving the maximal base-conservative augments?

In any event I don't see how category theory is helping here, indeed
this would seem to be an instance where category theory hinders more
than it helps.
-v