PhD Course - Category theory
Website: https://ctcourse2016.wikit.itu.dk/.
Organizer(s):
Rasmus Ejlers Møgelberg
Lecturer(s):
Rasmus Ejlers Møgelberg
Date(s) of the course:
September 9, 2016 - December 16, 2016.
A
total of 14 weekly lectures interrupted by fall break.
Time:
From 13:00 till 15:00
Room preferences:
4A58
Course description:
Category theory is an abstract branch of
mathematics which has found many applications, in particular in computer
science, logic and other fields of mathematics. For computer scientists and
logicians, category theory is useful because it provides a set of abstractions
useful for organising e.g. denotational models and also a set of tools for
constructing new such models. For example, forcing in set theory can be
understood via sheaf categories and many concepts in functional programming (e.g.
monads) can be described abstractly and studied in category theory. Recently,
models constructed using category theory have been used in the design of new
type theories, such as homotopy type theory and guarded dependent type theory.
In this course we will cover the basic concepts of category theory and
illustrate these with applications to denotational semantics of programming
languages and logic. The course thus forms a base for further studies of e.g.
categorical logic and denotational semantics, such as models of (homotopy or
guarded) type theory.
Programme:
2 hours of lectures every week. For topics, see
course webpage. We will cover Steve Awodeys book Category theory 2nd ed.
Prerequisites:
No
Exam:
There will be written exercises every week of which
students must have 3 out of 4 approved.
Credits:
7.5 ECTS
Amount of hours the student is expected to use on the course:
Participation: 28
Preparation: 182
How to sign up:
Write an email to mogel@itu.dk, Rasmus Ejlers Møgelberg.