Course detail

Basics of Category Theory

FSI-9TKDAcad. year: 2017/2018

The aim of the subject is to make students acquainted with fundamentals of the category theory with respect to applications, especially in computer science. Some important concrete applications will be discussed in greater detail.

Language of instruction

Czech

Number of ECTS credits

2

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Institute of Mathematics (ÚM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Not applicable.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

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

Not applicable.

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

M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990 (EN)
B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991 (EN)

Recommended reading

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

Type of course unit

 

Lecture

20 hours, 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