Symmetric containers

This talk will introduce symmetric containers, presenting their structure and basic results. Connections to related areas such as homotopy type theory and combinatorics will be outlined, and current research problems will be presented.
The notion of symmetric container arises naturally when studying endo-functors on the category of groupoids. Symmetric containers form a 2-category with products, sums and a differentiation operation enabling us to think of them as similar to power series with positive rational coefficients.
Among symmetric containers we find natural analogues of polynomials, rational functions and the exponential function. Examples of symmetric containers occur naturally in combinatorics as well as topology (by thinking of the fundamental groupoid as a first approximation to the homotopy type of a space).