240213 Léonard Guetta

Polygraphic homology was introduced in the 2000s by Métayer and his collaborators as a means to understand some combinatorial results on presentation of monoids. However, it was quickly understood that polygraphic homology, and more generally the theory of polygraphs (also known as computads), was a powerful tool that allowed to revisit the homology of monoids, groups and even categories, both on a practical and theoretical level. Furthermore, the theory of polygraphs can be naturally understood as a part of higher category theory, however from a slightly different perspective than the standard approach on the subject, which is of interest by itself. In this talk, I will give a broad introduction to polygraphic homology and the theory of polygraphs. I will start from the ground up by giving some motivation and simple examples and then present the subject from a more abstract perspective.