YaMCATS category theory seminars on Zoom next Friday, 5 Feb

YaMCATS category theory seminars on Zoom next Friday, 5 Feb

[Steve Vickers]

YaMCATS is the Yorkshire and Midlands Category Theory Seminars

    https://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-profiles/simona-paoli/yorkshire-and-midlands-category-theory-seminar-yamcats

Our next meeting, virtual by Zoom, will be hosted by Nicola Gambino at Leeds  University next Friday afternoon. Details and Zoom link below.

Nicola Gambino
Simona Paoli
Steve Vickers

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
Passcode: 683026

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)
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.

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