[-- Attachment #1.1: Type: text/plain, Size: 466 bytes --] I have seen these papers on the arXiv for a while now: https://arxiv.org/abs/1804.01413 https://arxiv.org/abs/1803.01709 Can anybody explain what they are about? -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. [-- Attachment #1.2: Type: text/html, Size: 736 bytes --]

[-- Attachment #1: Type: text/plain, Size: 542 bytes --] From vaugely skimming through it, it looks like they define a more explicit version of judgmental equality, from which they found an extensional type theory, and proceed to calculate the fundamental group of different spaces in that theory. -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout.

[-- Attachment #1: Type: text/plain, Size: 1076 bytes --] Hello, Roughly speaking, a quantum group is an algebraic structure which is obtained by means of a deformation of a group. There rigorous definition is here: https://ncatlab.org/nlab/show/quantum+group Official reference to quantum groups: Kassel, Christian (1995), Quantum groups, Graduate Texts in Mathematics, 155, Berlin, New York: Springer-Verlag, doi:10.1007/978-1-4612-0783-2, ISBN 978-0-387-94370-1, MR 1321145 Deformations... homotopy type... Well, given a "well-behaved" family of quantum groups, which are deformations of the same group, is it "natural" to define this family as a homotopy type? Is HoTT, in some way, a natural setting to work with quantum groups because types and homotopy types are identified? Kind Regards, José M. -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout. [-- Attachment #2: Type: text/html, Size: 1773 bytes --]

I doubt it. My understanding of quantum groups is that they are supposed to be groups with "noncommutative underlying spaces", and the homotopy types of HoTT are all "commutative" in this sense. On Mon, Oct 29, 2018 at 7:02 PM José Manuel Rodriguez Caballero <josephcmac@gmail.com> wrote: > > Hello, > Roughly speaking, a quantum group is an algebraic structure which is obtained by means of a deformation of a group. There rigorous definition is here: https://ncatlab.org/nlab/show/quantum+group > > Official reference to quantum groups: Kassel, Christian (1995), Quantum groups, Graduate Texts in Mathematics, 155, Berlin, New York: Springer-Verlag, doi:10.1007/978-1-4612-0783-2, ISBN 978-0-387-94370-1, MR 1321145 > > Deformations... homotopy type... Well, given a "well-behaved" family of quantum groups, which are deformations of the same group, is it "natural" to define this family as a homotopy type? Is HoTT, in some way, a natural setting to work with quantum groups because types and homotopy types are identified? > > Kind Regards, > José M. > > > -- > You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. > To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout.