Basics of Category Theory
FSI-9TKDAcad. year: 2020/2021
The aim of the subject is to make students acquainted with basic concepts and results of category theory with respect to their applications in various fields, particularly in computer science. They will be able to use the knowledge acquainted in their professional specializations.
Learning outcomes of the course unit
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.
Recommended optional programme components
Recommended or required reading
M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990 (EN)
J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982 (CS)
J. Adámek, Theory of Mathematical Structures, Springer 1983 (EN)
B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991 (EN)
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991 (EN)
S. MacLane: Categories for the Working Mathematician, Springer-Verlag 1971 (EN)
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and methods of the category theory including examples.
Assesment methods and criteria linked to learning outcomes
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.
Language of instruction
The goal of the subject is to get students acquainted with basics of the category theory and some of its applications in computer science.
Specification of controlled education, way of implementation and compensation for absences
Since the subject is taught in the form of a lecture, which is not compulsory for student, the attendance will not be checked.
Type of course unit
20 hours, optionally
Teacher / Lecturer
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
12.Cartesian closed categories and typed lambda-calculus
13.The cartesian closed category of Scott domains