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September 10, 2008

Who are Various?

Posted by David Corfield

If you’re in the Manchester area on Saturday 4 October with not much to do, why not join me at MIMS Workshop on New Directions in Philosophy of Mathematics? I’m talking there, and will be discussing what I’ve been writing for a contribution to a book on Lautman.

While looking at what can be seen of Lawvere’s Categories of Space and of Quantity article mentioned here, I remembered that Saunders Mac Lane had written the preceding article in the book – The Protean Character of Mathematics. In view of the fact that one of the cases Lautman treats is Galoisian duality, I was delighted to find on turning back the page in Google books that on page 13 he writes

Janelidze, 1988 Categorical formulation of Galois Structure

Various, 1990 One adjunction handles Galois and much more

Unfortunately, pages 11-12 are missing, but if memory serves, these two entries are just the end of a list starting out with Galois.

By ‘Janelidze, 1988’, is Mac Lane referring to

Galois theory in categories: the new example of differential fields, Proc. Conf. Categorical Topology in Prague 1988, World Scientific 1989, 369-380?

And who are ‘Various, 1990’, what is their single adjunction, and what is ‘much more’?

Posted at September 10, 2008 9:12 AM UTC

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11 Comments & 0 Trackbacks

Re: Who are Various?

Presumably, Janelidze’s abstract categorical Galois theorem is on Mac Lane’s mind.

Posted by: David Corfield on September 10, 2008 11:43 AM | Permalink | Reply to this

Re: Who are Various?

This categorical Galois theorem stuff sounds interesting, but browsing through the Google Books link you’ve given, I’m having trouble seeing the forest for the trees. Can someone give an overview? (I know a little bit of conventional Galois theory.)

Posted by: Jamie Vicary on September 10, 2008 12:23 PM | Permalink | Reply to this

Re: Who are Various?

Looks like we should get hold of Galois Theory in Variable Categories. Trouble is I only have access to Applied Categorical Structures post-1997.

Posted by: David Corfield on September 10, 2008 2:12 PM | Permalink | Reply to this

Re: Who are Various?

Try looking at “Galois Theories” by Borceux and Janelidze, Cambridge studies in advanced mathematics vol 72, Cambridge 2001, ISBN 0 521 80309 8.

It is a good introduction to the theory.

Posted by: Tim Porter on September 10, 2008 5:15 PM | Permalink | Reply to this

Re: Who are Various?

Looks like an excellent reason to come to Category Theory 2009 in sunny Cape Town!

pic

Posted by: Bruce Bartlett on September 10, 2008 2:24 PM | Permalink | Reply to this

Re: Who are Various?

Maybe ‘one adjunction hundles’ is a typo for ‘on adjunction bundles’?

Posted by: John Baez on September 10, 2008 4:29 PM | Permalink | Reply to this

Re: Who are Various?

Oh dear, I didn’t catch it at first but now I see it is hilarious!

Various, 1990 One adjunction hundles Galois and much more.

I’ve been working with adjunctions for a while now, but I had no idea they were capable of fighting back viciously and “hundling” a man… and even worse! This scares the heeby-jeebies out of me.

Posted by: Bruce Bartlett on September 10, 2008 4:46 PM | Permalink | Reply to this

Re: Who are Various?

I can’t be sure who’s joking here. Anyway, it’s corrected. Presumably I carried over the ‘un’ to the next word.

Posted by: David Corfield on September 10, 2008 5:52 PM | Permalink | Reply to this

All the Fleche is Grassmanian; Re: Who are Various?

“One adjunction handles Galois and much more”

Sad to say, one sword thrust handled Galois.

Good that he stayed up all night, writing equations of genius by candelight. And then went to his doom, over a combination of the set-up (honor of a whore) and the politics (Royalist versus Revolutionary). This would be SUCH a great movie. If I were making the “elevator pitch” to Spielberg, I’d say: “A Beautiful Mind meets The Three Musketeers!”

Posted by: Jonathan Vos Post on September 13, 2008 8:13 PM | Permalink | Reply to this

Re: All the Fleche is Grassmanian; Re: Who are Various?

I agree, it would make a great movie, in the hands of the right director. (Please, not Ron Howard!) Since most of the stories seem to be somewhat legendary anyway, one could probably replace pistols (as used in the actual duel) with swords and get away with it. And I like the idea of there being a whore behind the scenes (played by Julia Roberts?), although the woman Galois loved was apparently the daughter of a highly respected physician.

http://en.wikipedia.org/wiki/%C3%89variste_Galois#Final_days

Posted by: Todd Trimble on September 25, 2008 7:15 PM | Permalink | Reply to this

Re: Who are Various?

Even more reason to come to the Workshop. We have as a speaker Angus MacIntyre, the model theorist who believes Grothendieck has much to teach his field.

Posted by: David Corfield on September 25, 2008 10:05 AM | Permalink | Reply to this

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