Course detail

Category Theory in Computer Science

FIT-TKDAcad. year: 2024/2025

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.

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Dept. of Algebra and Discrete Mathematics (ÚM OAAG)

Entry knowledge

Basic lectures of mathematics at technical universities

Rules for evaluation and completion of the course

The subject is evaluated according to the result of the final exam, the minimum for passing the exam is 50/100 points.  

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.

 
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991

Classification of course in study plans

  • Programme DIT Doctoral 0 year of study, summer semester, compulsory-optional
  • Programme DIT Doctoral 0 year of study, summer semester, compulsory-optional
  • Programme DIT-EN Doctoral 0 year of study, summer semester, compulsory-optional
  • Programme DIT-EN Doctoral 0 year of study, summer semester, compulsory-optional

  • Programme CSE-PHD-4 Doctoral

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

  • Programme CSE-PHD-4 Doctoral

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

  • Programme CSE-PHD-4 Doctoral

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

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. RNDr. Josef Šlapal, CSc.

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 

Guided consultation in combined form of studies

26 hod., optionally

Teacher / Lecturer

prof. RNDr. Josef Šlapal, CSc.