ACT@UCR Seminar: Structured Cospans and Double Categories - John Baez скачать в хорошем качестве

ACT@UCR Seminar: Structured Cospans and Double Categories - John Baez

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. slides and more: http://math.ucr.edu/home/baez/structu... This talk on 2020 April 1 is part of the Applied Category Theory at U. C. Riverside Seminar: https://sites.google.com/ucr.edu/actucr/