This talk will cover the very basics of Category Theory, motivated by simple examples using the category of sets. I will then introduce some applications to other areas of mathematics, such as linear algebra and programming language theory.

Outline

• Introduction (definition of categories - objects, morphisms, with composition and identity)

• Examples with categories of sets (to illustrate compositions, retractions and sections, isomorphisms, other interesting morphisms, etc)

• Notion of initial, terminal and zero objects

• Categories of categories, locally small categories, functors (and some interesting ones), categorical equivalence

• Applications - linear algebra

• Applications - CS, Haskell, programming language theory