Marek Zawadowski: Equational Theories for Combinatorics and Geometry

Monads, Lawvere Theories, and Operads provide different means to define algebraic structures in categories. Under some natural assumptions they present the same algebraic structures in the category Set. Symmetric operads were originally introduced to study the geometry of loop spaces, whereas analytic and polynomial monads were introduced to study enumerative combinatorics. They have been applied with a success to combinatorial problems related to higher-dimensional categories.

In my talk I will discuss the subcategories of categories of monads (on Set) Lawvere theories, and operads (in Set) that correspond to various classes of equational theories relevant for combinatorics and geometry.