Course detail

Category Theory

FIT-TKDAcad. year: 2019/2020

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.

 

 

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

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

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech, English

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.

Classification of course in study plans

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, summer semester, 0 credits, optional

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

  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 

eLearning