Re: [FOM] Preprint: Topological Galois Theory
On 04 Jan 2013, at 02:34, meekerdb wrote: On 1/3/2013 5:06 PM, Stephen P. King wrote: Hi Bruno, You might be interested in this! How about giving us a 500 word summary including an example of it's application. Good point. It is not uninteresting, but is very technical, and as a foundation of math can be used for many things. Grothendieck's Galois theory would need a 50h course before we can say sensible things. I use much simpler math, but most people have already difficulties. Bruno Brent Original Message Subject:[FOM] Preprint: Topological Galois Theory Date: Thu, 3 Jan 2013 20:08:04 +0100 From: Olivia Caramello oc...@hermes.cam.ac.uk Reply-To: Foundations of Mathematics f...@cs.nyu.edu To: Foundations of Mathematics f...@cs.nyu.edu Dear All, The following preprint is available from the Mathematics ArXiv at the address http://arxiv.org/abs/1301.0300 : O. Caramello, Topological Galois Theory Abstract: We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group. Our framework subsumes in particular Grothendieck's Galois theory and allows to build Galois-type equivalences in new contexts, such as for example graph theory and finite group theory. This work represents a concrete implementation of the abstract methodologies introduced in the paper The unification of Mathematics via Topos Theory, which was advertised on this list two years ago. Other recent papers of mine applying the same general principles in other fields are available for download at the address http://www.oliviacaramello.com/Papers/Papers.htm . Best wishes for 2013, Olivia Caramello No virus found in this message. Checked by AVG - www.avg.com Version: 2013.0.2805 / Virus Database: 2637/6007 - Release Date: 01/03/13 -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything- l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Fwd: [FOM] Preprint: Topological Galois Theory
On 1/3/2013 8:34 PM, meekerdb wrote: On 1/3/2013 5:06 PM, Stephen P. King wrote: Hi Bruno, You might be interested in this! How about giving us a 500 word summary including an example of it's application. Hi Brent, I guess that you can't be bothered to read it for yourself. OK, but why advertize the fact? I guess you don't understand category theoretical stuff... OK. Section 6.3 and 6.4 are very nice formal treatments of the idea that I am exploring, the Stone duality thing that I am often sputtering on and on about. ;-) My idea is that Boolean algebras can evolve via non-exact homomorphsims. ;-) I just don't happen to think or write in formal terms. Brent Original Message Subject:[FOM] Preprint: Topological Galois Theory Date: Thu, 3 Jan 2013 20:08:04 +0100 From: Olivia Caramello oc...@hermes.cam.ac.uk Reply-To: Foundations of Mathematics f...@cs.nyu.edu To: Foundations of Mathematics f...@cs.nyu.edu Dear All, The following preprint is available from the Mathematics ArXiv at the addresshttp://arxiv.org/abs/1301.0300 : O. Caramello, Topological Galois Theory Abstract: We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group. Our framework subsumes in particular Grothendieck's Galois theory and allows to build Galois-type equivalences in new contexts, such as for example graph theory and finite group theory. This work represents a concrete implementation of the abstract methodologies introduced in the paper The unification of Mathematics via Topos Theory, which was advertised on this list two years ago. Other recent papers of mine applying the same general principles in other fields are available for download at the addresshttp://www.oliviacaramello.com/Papers/Papers.htm . Best wishes for 2013, Olivia Caramello -- Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Fwd: [FOM] Preprint: Topological Galois Theory
Hi Bruno, You might be interested in this! Original Message Subject:[FOM] Preprint: Topological Galois Theory Date: Thu, 3 Jan 2013 20:08:04 +0100 From: Olivia Caramello oc...@hermes.cam.ac.uk Reply-To: Foundations of Mathematics f...@cs.nyu.edu To: Foundations of Mathematics f...@cs.nyu.edu Dear All, The following preprint is available from the Mathematics ArXiv at the address http://arxiv.org/abs/1301.0300 : O. Caramello, Topological Galois Theory Abstract: We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group. Our framework subsumes in particular Grothendieck's Galois theory and allows to build Galois-type equivalences in new contexts, such as for example graph theory and finite group theory. This work represents a concrete implementation of the abstract methodologies introduced in the paper The unification of Mathematics via Topos Theory, which was advertised on this list two years ago. Other recent papers of mine applying the same general principles in other fields are available for download at the address http://www.oliviacaramello.com/Papers/Papers.htm . Best wishes for 2013, Olivia Caramello -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Fwd: [FOM] Preprint: Topological Galois Theory
On 1/3/2013 5:06 PM, Stephen P. King wrote: Hi Bruno, You might be interested in this! How about giving us a 500 word summary including an example of it's application. Brent Original Message Subject:[FOM] Preprint: Topological Galois Theory Date: Thu, 3 Jan 2013 20:08:04 +0100 From: Olivia Caramello oc...@hermes.cam.ac.uk Reply-To: Foundations of Mathematics f...@cs.nyu.edu To: Foundations of Mathematics f...@cs.nyu.edu Dear All, The following preprint is available from the Mathematics ArXiv at the addresshttp://arxiv.org/abs/1301.0300 : O. Caramello, Topological Galois Theory Abstract: We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group. Our framework subsumes in particular Grothendieck's Galois theory and allows to build Galois-type equivalences in new contexts, such as for example graph theory and finite group theory. This work represents a concrete implementation of the abstract methodologies introduced in the paper The unification of Mathematics via Topos Theory, which was advertised on this list two years ago. Other recent papers of mine applying the same general principles in other fields are available for download at the addresshttp://www.oliviacaramello.com/Papers/Papers.htm . Best wishes for 2013, Olivia Caramello No virus found in this message. Checked by AVG - www.avg.com http://www.avg.com Version: 2013.0.2805 / Virus Database: 2637/6007 - Release Date: 01/03/13 -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
