Course detail

Category Theory

FIT-TKDAcad. year: 2017/2018

Small and large categories, algebraic structures as categories, constructions on categories (free categories, subcategories and dual categories), special types of objects and morphisms, products and sums of objects, categories with products and circuits, categories with sums and flow charts, distributive categories and imperative programs, data types (arithmetics of reals, stacks, arrays, Binary trees, queues pointers, Turing Machines), functors anf functor categories, directed graphs and regular grammars.

 

 

Language of instruction

Czech

Mode of study

Not applicable.

Learning outcomes of the course unit

The students will be acquainted with the fundamental principles of the category theory and with possibilities of applying these principles in computer science. They will be able to use the knowledges gained when solving concrete problems in their specializations.

Prerequisites

Basic lectures of mathematics at technical universities

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Course curriculum

    Syllabus of lectures:
    1. Small and large categories
    2. Algebraic structures as categories
    3. Constructions on categories
    4. Properties of objects and morphisms
    5. products and sums of objects
    6. Categories with products and circuits
    7. Categories with sums and flow charts
    8. Distributive categories
    9. Imperative programs
    10. Data types stack, array and binyry tree
    11. Data types queue and pointer, Turing machines
    12. Functors anf functir categories 
    13. Grammars and automata 

Work placements

Not applicable.

Aims

The aim of the subject is to make students acquainted with fundamentals of the category theory oriented on applications in computer science. Individual categorical concepts and results are discussed from the view point of their meaning and use in computer science.

 

Specification of controlled education, way of implementation and compensation for absences

Written essay completing and defending.

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 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

Recommended reading

J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982 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

Classification of course in study plans

  • Programme CSE-PHD-4 Doctoral

    branch DVI4 , 0 year of study, winter semester, elective