Fusion categories and their various generalisations appears in many area of mathematics and physics. They are related to fusion rules in conformal field theories, to topological defects in anyonic field theories, to the geometric invariants of topological field theories, etc. I will present an introduction to this subject, in which I will assume no prior knowledge of categories in general. I will then present ongoing work on building a generalised fusion category from Temperley-Lieb algebras, which appear for instance in integrable lattice models, some of which are conjectured to become logarithmic CFTs in their continuum limit.

IPhT