Resumen:

I will introduce an interesting connection between the theory of Hopf monoids in combinatorics and Möbius inversion. A Hopf monoid is an algebraic abstraction of families of combinatorial objects which have an operation which combines objects and an operation which breaks objects apart. Like many algebraic structures, Hopf monoids have a nice notion of duality. We will show that for many combinatorial families, this notion of duality can be interpreted using Möbius inversion over some partial order. We will focus on the cases of set partitions, graphs, and matroids