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John Baez (Jan 31 2021 at 20:26):Here's the schedule of the Friday February 5th 2021 meeting of the Yorkshire and Midlands Category Theory Seminar. There will be three talks.
YaMCATS - Friday 5th February - University of Leeds (via Zoom)
All times are UK (GMT = UTC+00:00).
14:30-15:30 Martin Escardo (University of Birmingham), Equality of mathematical structures
15:30-16:30 Sina Hazratpour (University of Leeds), Kripke-Joyal semantics for dependent type theory
16:30-17:00 Break
17:00-18:00 John Baez, Structured versus decorated cospans
Zoom links
Nicola Gambino is inviting you to a scheduled Zoom meeting.
Topic: YaMCATS 23
Time: Feb 5, 2021 02:30 PM London
Join Zoom Meeting
https://universityofleeds.zoom.us/j/81042397132?pwd=RTg3MFV1TUt2YzJXZVZJSkhoOEQwQT09
Meeting ID: 810 4239 7132
use this number to get in: 68302x where x is a perfect number
Abstracts
Martin Escardo
Title: Equality of mathematical structures
Abstract. Two groups are regarded to be the same if they are isomorphic, two topological spaces are regarded to be the same if they are homeomorphic, two metric spaces are regarded to be the same if they are isometric, two categories are regarded to be the same if they are equivalent, etc. In Voevodsky's Univalent Foundations (HoTT/UF), the above become theorems: we can replace "are regarded to be the same” by "are the same". I will explain how this works. I will not assume previous knowledge of HoTT/UF or type theory.
Sina Hazratpur (University of Leeds)
Title: Kripke-Joyal semantics for dependent type theory
Abstract. Every topos has an internal higher-order intuitionistic logic. The so-called Kripke–Joyal semantics of a topos gives an interpretation to formulas written in this language used to express ordinary mathematics in that topos. The Kripke–Joyal semantics is in fact a higher order generalization of the well-known Kripke semantic for intuitionistic propositional logic. In this talk I shall report on joint work with Steve Awodey and Nicola Gambino on extending the Kripke–Joyal semantics to dependent type theories, including homotopy type theory.
John Baez (University of California at Riverside)
Title: Structured versus decorated cospans
Abstract. One goal of applied category theory is to understand open systems: that is, systems that can interact with the external world. We compare two approaches to describing open systems as cospans equipped with extra data: structured and decorated cospans. Each approach provides a symmetric monoidal double category, and we prove that under certain conditions these symmetric monoidal double categories are equivalent. We illustrate these ideas with applications to dynamical systems and epidemiological modeling. This is joint work with Kenny Courser and Christina Vasilakopoulou.
David Michael Roberts (Jan 31 2021 at 22:29):They all look like really good talks. I rue the timezone difference between here and the UK...
That said, Simona once offered for me to give a talk at YAMCaTS, if I was ever in the UK, so I guess now I can be, via Zoom :-)
John Baez (Jan 31 2021 at 22:45):I'm asking them to record my talk, and it'd be good if they recorded everyone's talk - or at least, everyone who is okay with that.