Discussion of Homotopy Type Theory and Univalent Foundations
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* [HoTT] YaMCATS 24 - April 29th, 2021
@ 2021-04-22 10:36 Nicola Gambino
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From: Nicola Gambino @ 2021-04-22 10:36 UTC (permalink / raw)
  To: homotopytypetheory

*** Yorkshire and Midlands Category Theory Seminar
*** Thursday 29th April, 2:00-5:30pm (UK time)
*** via Zoom

Dear all,

I am pleased to announce the 24th meeting of the Yorkshire and Midlands Category Theory Seminar, to be held online on Thursday 29th April, 2:00-5:30pm (UK time). 

The program will be as follows:

2:00-3:00 Karol Szumilo (Leeds), Infty-groupoids in lextensive categories
3:00-4:00 Anna Laura Suarez (Universite’ Cote, d’Azur), The category of finitary biframes as the category of pointfree bispaces
4:00-5:00 Ivan Di Liberti (Czech Academy of Sciences), Formal model theory and Higher Topology. 
5:00-5:30 Tea/coffee

Please see below for abstracts. The Zoom link is 

Join Zoom Meeting: https://universityofleeds.zoom.us/j/88049499094?pwd=UEVyTEdDWnZyV2NNMGNwaTBaaDlSZz09
Meeting ID: 880 4949 9094
Passcode: Z*9qfq

Please do not post the Zoom link on websites. 

With best regards,
Nicola

==
Karol Szumilo (Leeds), Infty-groupoids in lextensive categories

Abstract: I will discuss a construction of a new model structure on
simplicial objects in a countably lextensive category (i.e., a category
with well behaved finite limits and countable coproducts). This builds
on previous work on a constructive model structure on simplicial sets,
originally motivated by modelling Homotopy Type Theory, but now
applicable in a much wider context. This is joint work with Nicola
Gambino, Simon Henry and Christian Sattler.


==
Anna Laura Suarez (Universite’ Cote, d’Azur), The category of finitary biframes as the category of pointfree bispaces

Bitopological spaces have found numerous applications: they appear naturally when dealing with uniform spaces (already introduced by Weil in [1]), as well as providing a particularly elegant view of Priestley duality (see [4], but also [3]). We explore the theory of finitary biframes, introduced in [5], as a category of pointfree bitopological spaces. In particular, we compare it to the existing theory of biframes ([2]) and the more recent one of d-frames ([4]). We illustrate some of the advantages that finitary biframes present when compared to both biframes and d-frames. One of the main strengths of the theory of finitary biframes is that for every finitary biframe L one may construct a finitary biframe A(L) whose main component is order-isomorphic to the collection of all quotients of L.

[1] Andre', W. Sur les espaces a structure uniforme et sur la topologie generale / par Andre' Weil. Actualites scientifiques et industrielles. Hermann et cie, Paris, 1937.
[2] Banaschewski, B., Brummer, G. C., and Hardie, K. A. Biframes and bispaces. Quaestiones Mathematicae 6, 1-3 (1983), 13–25.
[3] Bezhanishvili, G., Bezhanishvili, N., Gabelaia, D., and Kurz, A. Bitopological duality for distributive lattices and Heyting algebras. Mathematical Structures in Computer Science 20, 3 (2010), 359–393.
[4] Jung, A., and Moshier, M. A. On the bitopological nature of Stone duality. Tech. Rep. CSR-06-13, University of Birmingham, 2006. 110 pages.


==
Ivan Di Liberti (Czech Academy of Sciences), Formal model theory and Higher Topology. 

Abstract. Motivated by the abstract study of semantics, we study the interaction between topoi, accessible categories with directed colimits and ionads. This theory amounts to a categorification of famous construction from general topology: the Scott topology on a poset and the adjunction between locales and topological spaces. This technology is then used in order to establish syntax-semantics dualities. Among the significant contributions, we provide a logical understanding of ionads that encompasses Makkai ultracategories. 

References.
PhD thesis, arXiv:2009.07320.
General facts on the Scott Adjunction, ArXiv:2009.14023.
Towards Higher Topology, ArXiv:2009.14145.
Formal Model Theory & Higher Topology, ArXiv:2010.00319.


==
Dr Nicola Gambino
Associate Professor in Pure Mathematics and Director of Research and Innovation
School of Mathematics, University of Leeds
Dr Nicola Gambino
Associate Professor in Pure Mathematics and Director of Research and Innovation
School of Mathematics, University of Leeds

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2021-04-22 10:36 [HoTT] YaMCATS 24 - April 29th, 2021 Nicola Gambino

Discussion of Homotopy Type Theory and Univalent Foundations

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