Title:

# Category Theory

Code:TKD
Ac.Year:2003/2004
Sem:Summer
Language of Instruction:Czech
Completion:examination (written)
Type of
instruction:
Hour/semLecturesSeminar
Exercises
Laboratory
Exercises
Computer
Exercises
Other
Hours:390000
ExamsTestsExercisesLaboratoriesOther
Points:00000
Guarantor:Šlapal Josef, prof. RNDr., CSc. (DADM)
Lecturer:Šlapal Josef, prof. RNDr., CSc. (DADM)
Instructor:Šlapal Josef, prof. RNDr., CSc. (DADM)
Faculty:Faculty of Information Technology BUT

Learning objectives:
The aim of the subject is to make students acquainted with fundamentals of the category theory with respect to applications to computer science. Some important concrete applications will be discussed in greater detail.
Description:
Graphs and categories, algebraic structures as categories, constructions on categories (subcategories and dual categories), special types of objects and morphisms, products and sums of objects, natural numbers objects, deduction systems, functors and diagrams, functor categories, grammars and automata, natural transformations, limits and colimits, adjoint functors, cartesian closed categories and typed lambda-calculus, the cartesian closed category of Scott domains.
Learning outcomes and competencies:
The students will be acquainted with the fundamental principles of the category theory and with possibilities of applying these principles to computer science. They will be able to use the knowledges gained when solving concrete problems in their specializations.
Syllabus of lectures:

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
12. Cartesian closed categories and typed lambda-calculus
13. The cartesian closed category of Scott domains
Fundamental literature:

1. M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990
2. B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
3. R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
Study literature:

1. J. Adámek, Mathematical Structures and Categories (in Czech), SNTL, Prague, 1982
2. B.C. Pierce, Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
3. R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991