Category Theory in Computer Science

• 26 hrs lectures

• 100 pts final exam

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.

Basic lectures of mathematics at technical universities

• 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

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 

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