# Philip Scott

Traced categories: algebraic structure of feedback and partial feedback in networks

In the late '80s/early '90s an algebraic structure dealing with cyclic operations emerged from various fields, including flowchart schemes, dataflow networks with feedback, action calculi, proof theory, as well as algebraic topology and knot theory. This structure is now known as a "traced monoidal category" , after the influential paper of Joyal, Street and Verity, who studied such categories in pure mathematics, but with an eye to applications in many fields. The concept also occurs as a basic structure in network algebra. Since then, these categories have been studied, with variations, in many areas of mathematics, logic and theoretical computer science, Recently, there has been a trend to consider partial traces and trace ideals; indeed it appears that such algebraic structures may be relevant to several areas, including biology and physics, or indeed to any field where cyclic networks are used. We give a leisurely introduction to the algebra, with many examples. This can be considered an introduction to a later, more detailed series of talks.