Course detail

Basics of Category Theory

FSI-9TKDAcad. year: 2022/2023

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.

Language of instruction

Czech, English

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Institute of Mathematics (ÚM)

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.

Prerequisites

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.

Co-requisites

Not applicable.

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.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982 (CS)
J. Adámek, Theory of Mathematical Structures, Springer 1983 (EN)
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991 (EN)

Classification of course in study plans

  • Programme D-APM-K Doctoral 1 year of study, winter semester, recommended course
  • Programme D-APM-P Doctoral 1 year of study, winter semester, recommended course

Type of course unit

 

Lecture

20 hod., optionally

Teacher / Lecturer

prof. RNDr. Josef Šlapal, CSc.

Syllabus

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