YaMCATS 24 - April 29th, 2021

[Nicola Gambino <n.gambino@leeds.ac.uk>]

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


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