Sorry, and thanks to Jon for noticing the slip of terminology in my mail. Indeed, Bénabou was insisting on the importance of his notion of definability. Francis *********************************** Francis Borceux 6 rue François 1490 Court-Saint-Étienne Belgique Fixe: +32(0)10614205 Mobile: +32(0)478390328 ---------- You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27
Ungated link to the 1985 JSL paper (see p35 for definition of definability): https://protect-au.mimecast.com/s/Y-NsC2xMRkUwx1OqunZtxI?domain=artscimedia.... Sent
On Jan 22, 2024, at 12:00 PM, Francis Borceux <francis.borceux@uclouvain.be> wrote:
Sorry, and thanks to Jon for noticing the slip of terminology in my mail.
Indeed, Bénabou was insisting on the importance of his notion of definability.
Francis
*********************************** Francis Borceux 6 rue François 1490 Court-Saint-Étienne Belgique Fixe: +32(0)10614205 Mobile: +32(0)478390328
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Thanks for that "ungated" link to Bénabou's 1985 JSL paper, Wes. As it turned out, I'd downloaded all 28 pages back in 2011, I can't remember why. Moreover it arrived 26 years earlier in my mailbox in 1985, but who reads every article, especially if you're more on the universal algebra side than the category theory side in 1985. Now that it's 2024, what I'm wondering is, is there 28 pages of useful information there? I appreciate the idea of a fibration as a functor C → B where B is a "base category" looking enough like *Set* (aka *Ens*). In recent years I've been writing about the Yoneda embedding as a way of viewing Chu spaces over *Set*, namely as Set-valued functors representing structured objects. This sort of thing is closer to toposes than abelian categories, both of which I like a lot given that the Big Bang seems to have evolved from a topos to (at least in our neighborhood) an abelian category. What I'm having difficulty with is why Jean took 28 pages to make his point. It seemed better suited to the Journal of Philosophical Logic than to JSL. I'm a great fan of Einstein's "make everything as simple as possible but no simpler". However that implies that there's a boundary, and in the case of fibrations and definability, I'm not at all clear as to where that boundary should be drawn. Vaughan Pratt https://protect-au.mimecast.com/s/3wnSC81Vq2CRLlpYinMtKz?domain=clim8.stanfo... On Mon, Jan 22, 2024 at 4:03 PM Wesley Phoa <doctorwes@gmail.com> wrote:
Ungated link to the 1985 JSL paper (see p35 for definition of definability): https://protect-au.mimecast.com/s/dV7XC91W8rCB9vE2CEg1qQ?domain=artscimedia....
Sent
On Jan 22, 2024, at 12:00 PM, Francis Borceux < francis.borceux@uclouvain.be> wrote:
Sorry, and thanks to Jon for noticing the slip of terminology in my mail.
Indeed, Bénabou was insisting on the importance of his notion of definability.
Francis
*********************************** Francis Borceux 6 rue François 1490 Court-Saint-Étienne Belgique Fixe: +32(0)10614205 Mobile: +32(0)478390328
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Dear Vaughan, Benabou"s JSL paper is certainly more of a philosophical character than a mathematical one. But philosophical issues can be relevant and in this case definitely are. I think the following analogy might be helpful. Using strong choice principles every vector space can be endowed with a basis. But nobody thinks that they should form part of the definition or even be preserved by morphisms between them. And so it is with Grothendieck fibrations. They are the right notion but one may choose cleavages. However, they are not part of the structure and certainly should not be preserved by morphism, i.e. cartesian functors. Thomas ---------- You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=6bf90c14-94d1-45b7-a0b5-9dd447734d27
participants (4)
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Francis Borceux -
Thomas Streicher -
Vaughan Pratt -
Wesley Phoa