Course pages 2016–17

# Category Theory and Logic

## Lecture slides and notes

- lecture 1 (7 Oct)
- lecture 2 (10 Oct)
- lecture 3 (14 Oct)
- lecture 4 (17 Oct)
- lecture 5 (21 Oct)
- lecture 6 (24 Oct)
- Brief notes on the category theoretic semantics of Simply Typed Lambda Calculus

## Lecture summaries

**Lecture 1:**Introduction; some history; content of this course. Definition of category. The category of sets and functions. Commutative diagrams. Alternative definitions of category.**Lecture 2:**Examples of categories: pre-ordered sets and monotone functions; monoids and monoid homomorphisms; a pre-ordered set as a category; a monoid as a category. Definition of isomorphism.**Lecture 3:**Terminal objects. The opposite of a category and the duality principle. Initial objects. Free monoids as initial objects.**Lecture 4:**Binary products and coproducts.**Lecture 5:**Exponential objects: in the category of sets and in general. Cartesian closed categories: definition and examples.**Lecture 6:**Intuitionistic Propositional Logic (IPL) in Natural Deduction style. Semantics of IPL in a cartesian closed pre-ordered set.

## Exercise sheets

## Office hours

- The module lecturer will be available to answer questions about the
course material and exercises
**on Wednesdays between 12:00 and 13:00 in FC08 during Full Term**.

## Additional material

- The following is the classic text on category theory and is
definitely worth looking at if you are feeling mathematically
mature:
Mac Lane, Saunders.

*Categories for the Working Mathematician*. Graduate Texts in Mathematics 5, second ed. (Springer, 1988), ISBN 0-387-98403-8. - A student-oriented guide to on-line material on Category Theory is available at http://www.logicmatters.net/categories/.
- The Category Theory Seminar is held at 2.15pm on Tuesdays in Room MR5 of the Centre for Mathematical Sciences.
- Julia Goedecke's Category Theory course for the 2013/4 Mathematical Tripos Part III / Masters of Mathematics.
- Category Theory in the nLab.
- The Catsters' Category Theory Videos.
- Eugenia Cheng's book on
*Cakes, Custard and Category Theory*(published in the US under the title "How to Bake Pi").