Title: Props and Distributive Laws

Abstract:

In this talk, I will review Lack’s technique of composing props, and give examples thereof.

Many well-known concrete structures are presented by props; for example, (FinSet,+) is presented by the prop for the free commutative monoid. And by composing this prop with its opposite category using Lack’s technique, we obtain either bicommutative bialgebras or bicommutative Frobenius algebras, which are presentations for spans or cospans of finite sets, respectively—depending on the direction we compose things.

This modular process of building up props continues, eventually yielding much more complex structures. I intend to continue this process of building up props to the point where a fragment of the ZH calculus is obtained.