Introduction to Category Theory
, University of Nottingham
Category theory is a mathematical approach to the study of algebraic
structure that has become an important tool in theoretical computing
science, particularly for semantics-based research.
The aim of this
course is to teach the basics of category theory, in a way that is
accessible and relevant to computer scientists. The emphasis is on
gaining a good understanding the basic definitions, examples, and
techniques, so that students are equipped for further study on
their own of more advanced topics if required.
(what is category theory,
why is it useful,
why is it useful to computing,
examples of categories);
labelled graph homomorphisms,
examples of functors,
functors as arrows,
functors with two arguments);
- Natural transformations
natural transformations as arrows,
the Godement calculus);
- Special constructions
- Case study
(algebras, homomorphisms, homomorphisms as arrows, initial
algebras, catamorphisms, fusion, banana split).
There are also some
exercises for each lecture.