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Course detail

Basics of Category Theory

Course unit code: FSI-9TKD
Academic year: 2016/2017
Year of study: Not applicable.
Semester: winter
Number of ECTS credits:
Learning outcomes of the course unit:
Not applicable.
Mode of delivery:
Not applicable.
Prerequisites:
Not applicable.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
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.
Recommended or required reading:
M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990
J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982
B.C. Pierce, Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
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:
Not applicable.
Language of instruction:
Czech, English
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
Not applicable.
Specification of controlled education, way of implementation and compensation for absences:
Not applicable.

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

The study programmes with the given course