• a 2-category is a higher category, where on top of the objects and morphisms, there are also 2-morphisms between 1-morphisms.
• consists of:
  • objects
  • morphisms between objects
  • 2-morphisms between morphisms
• composition
  • the morphisms can be composed along objects
  • the 2-morphisms can be composed in two different directions:
    • horizontal: along objects
    • vertical: along morphisms
• provides the context for discussion adjunctions and monads