Modul: MAT075 Zurich Graduate Colloquium

## What is... a combinatorial presheaf?

Raúl Penaguião talk

**Date:** 26.11.19 **Time:** 17.15 - 18.30 **Room:**

The study of substructures in combinatorics is seminal in mathematics: a striking example is the characterization of planar graphs through its description of minors due to Kuratowski. Lately there has been a new construction of a Hopf algebra from patterns in permutations: that is, an algebraic object that is ideal to encode the notion of merging and splitting. We start our journey to encode substructures of permutations in a categorical way through combinatorial presheaves, that will bring us from category theory to factorization trees. Finally, we observe that the pattern Hopf algebra construction for permutations is not really restricted to permutations, but to any combinatorial object that allows for substructures.