This chapter is used to present the necessary background on category theory. The structures occurring in the later sections are introduced and their key properties are discussed. All of the definitions are illustrated by collections of examples, chosen by their relevance in the applications in the later sections. First some basic notions such as category, functor and natural transformation are defined and operations with them are explained. This allows for the introduction of adjunctions and monads. The Eilenberg–Moore category of a monad is defined together with the key concept of lifting of functors, natural transformations and adjunctions to Eilenberg–Moore categories of monads.