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John Baez (Mar 26 2020 at 23:55):Just to remind everyone:
John Baez (Mar 26 2020 at 23:55):This will be at 5 pm UTC, which is 10 am in California or 1 pm on the east coast of the United States, or 6 pm in England. It will be held online via Zoom, here:
https://ucr.zoom.us/j/607160601
unless Zoom is overwhelmed and we need to switch to YouTube. Discussion will be here on Zulip, and maybe also breakout rooms on Zoom.
Abstract. One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce “structured cospans” as a way to study networks with inputs and outputs. Given a functor L: A → X, a structured cospan is a diagram in X of the form
L(a) → x ← L(b).
If A and X have finite colimits and L is a left adjoint, we obtain a symmetric monoidal category whose objects are those of A and whose morphisms are certain equivalence classes of structured cospans. However, this arises from a more fundamental structure: a symmetric monoidal double category where the horizontal 1-cells are structured cospans, not equivalence classes thereof. We explain the mathematics and illustrate it with an example from epidemiology.
John Baez (Mar 26 2020 at 23:58):(I decided an example from epidemiology would be timely. I am not claiming we can cure coronavirus using double categories.)