Categories for the practising physicist

In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mainly symmetric ones, for which we propose a physical interpretation. Special attention is given to the category of sets and relations, posetal categories, diagrammatic calculi, strictification, compact categories, biproduct categories and abstract matrix calculi, internal structures, and topological quantum field theories. In our attempt to complement the existing literature we (on purpose) omitted some very basic topics for which we point to other available sources.