Category Theory

Recommended Prerequisites

Groups and Symmetries; Topology and Linear Analysis

Teaching Methods

The concepts and basic techniques of this course are introduced through several examples from diverse areas of mathematics. The focus is on the unification and economy of arguments resulting from the use of the language and techniques of this theory, and on the translation of problems between different fields. The students are guided towards the formulation and solution of problems, the search for examples and applications.

Some tutorial support will be available to help the students solving the proposed tasks.

Learning Outcomes

This course is an introduction to Category Theory, with focus on the basic categorical notions and techniques and some of its applications, namely to Algebra, Logic and Topology.

Work Placement(s)

No

Syllabus

Categories, functors and natural transformations.

Elementary properties of objects and morphisms of a category.

Limits and colimits. Construction of limits via products and equalizers. Preservation, reflection and creation of limits.

Representability: Yoneda Lemma and Yoneda embedding. Representable functors.

Adjoint functors. Cartesian closed categories.

Special categories, eg topos, abelian categories.

Head Lecturer(s)

Ivan Yudin

Assessment Methods

Assessment
There are two types of grading: during the semester or by final exam. Evaluation during the semester includes one or more mid-term exams (75-100%) and presentations, or solution of homework problems (0-25%).: 100.0%

Bibliography

S. MacLane, Categories for the Working Mathematician, Springer-Verlag, 1998.

F. Borceux, Handbook of Categorical Algebra, Vol I, Cambridge University Press, 1994.

M. Barr, C. Wells, Category Theory for Computing Science, Prentice Hall, 1990.