[pl-seminar] PL Seminar - Intro to Category Theory

[Calvin Smith <cjsmith@xxxxxxxxxxx>]

Howdy yâall,

This next Monday (03/18/2019) at noon in CS 4310, John Cyphert will lead an informal discussion on the basics of category theory. The abstract is below.

- Calvin

Abstract: In this talk I am going to be discussing the basics of category theory. Category theory is a branch of mathematics that formalizes mathematical structure. Category theory has built up quite a reputation for having quite powerful applications across a vast part of mathematics and programming languages. I imagine you have or will run into category theory concepts during your career. For example, categorical semantics, monads, functors, and proof assistants have deep connections to category theory. Maybe you've even had a collaborator say when explaining a concept to you "... to gain intuition from category theory ...", or you've heard the phrase "a monad is just a monoid in the category of endofunctors. What's the problem?" in response to the question what is a monad. In this lecture I will try and give a basic intro into some of this "general abstract nonsense" using examples and motivations from functional programming. I plan to at least talk about the following concepts

- Categories

  - Objects

  - Morphisms

  - Examples

- Initial and Terminal objects

- Products and Co-Products

- Functors if we have time