Title: Category Theory with Applications to Dynamical Systems
Abstract: In this talk we will examine an article by paper by John C. Baez andBlake S. Pollard: "A Compositional Framework for Reaction Networks" available at https://arxiv.org/pdf/1704.02051.pdf. This article presents a categorical approach to dynamical systems. Traditionally reaction networks with rates are formulated in terms of first-order differential equations and are usually referred to as rate equations. We will start with a brief introduction to category theory in order to introduce the tools used to define open rate equations. Then we will redefine rate equations categorically and we will introduce and discuss the category Dynam, the category of dynamical systems, whose objects are finite sets and morphisms are equivalence classes of dynamical systems. Finally, we will look at applications in Dynam to chemistry, disease modeling, and electrical engineering.