# Programming Languages and Tools Lab

## Summer School on Category Theory

**Instructor: **Prof. John Power, University of Bath, UK.

### General Information

The school will be carried out in English, attendance is free of charge, but the number of participants is potentially limited. The exact time and venue will be announced later.

To register for the school and receive future announces please join the following group:

https://groups.google.com/forum/#!forum/jbr_summer_school_on_category_theory

### Synopsis

Category Theory lies at the border of logic with algebra. It arose from algebraic topology in the 1940's and it continues to see application there. Since at least the 1970's, it has also been applied to and informed by computer science. In this course, motivated by computer science, and with examples primarily arising from computer science, we will introduce and explore some of the main themes of category theory.

No prior knowledge beyond familiarity with sets and functions is required for the course: we will establish at the start what participants know and we will work from there. For those participants with background in theoretical computer science, one sensible view of the course would be to see it as providing a mathematical foundation for the work in the Winter 2017 school on Denotational Semantics; but, as mentioned above, such knowledge is not requisite.

I expect to focus on the following five themes, corresponding broadly to the five days of the course:

1. what does it mean to have a left adjoint?

2. how can one use category theory to model universal algebra?

3. what is an enriched category?

4. how does one handle size issues such as the paradox of the set of all sets?

5. what is a 2-category?

In case you would like to read a little in advance, the single best text I know on category theory for computer scientists is Michael Barr and Charles Wells, Category Theory for Computing Science Third Edition, Les Publications CRM, 1999, ISBN 2-921120- 31-3 which is freely available at http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf