CAUTION: The Sender of this email is not from within Dalhousie. YaMCATS is the Yorkshire and Midlands Category Theory Seminars https://www2.le.ac.uk/departments/mathematics/extranet/staff-material/staff-... 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=RTg3MFV1TUt2YzJXZVZJSkho... 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. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]