This talk on Category Theory was held on Friday October 21, 2016 in MC 4020. The talk was given by Luthfi Mawarid.
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.
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