Basics of Category Theory

• 20 hrs lectures

The goal of the subject is to get students acquainted with basics of the category theory and some of its applications in computer science.
Students will get basic knowledge of the category theory and will learn using them for solving some problems of computer science like creating logic circuits and flow charts.

The knowledge is expected of the subjects General Algebra and Methods of discrete mathematics taught within the Bachelor's level and Graph theory and Mathematical structures taught within the Master's level of the study programme mathematical Engineering.

• J. Adámek, Theory of Mathematical Structures, Springer 1983
• R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991

• M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990
• B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
• S. MacLane: Categories for the Working Mathematician, Springer-Verlag 1971

1. Graphs and categories
2. Algebraic structures as categories
3. Constructions on categories
4. Properties of objects and morphisms
5. Products and sums of objects
6. Natural numbers objects and deduction systems
7. Functors and diagrams
8. Functor categories, grammars and automata
9. Natural transformations
10.Limits and colimits
11.Adjoint functors
12.Cartesian closed categories and typed lambda-calculus
13.The cartesian closed category of Scott domains

Students are to pass an exam consisting of the written and oral parts. During the exam, their knowledge of the concepts introduced and of the basic propertief of these concepts will be assessed. Also their ability to use theoretic results for solving concrete problems will be evaluated.
Since the subject is taught in the form of a lecture, which is not compulsory for student, the attendance will not be checked.

During teaching the students are in personal contact with the teacher.