Title:

# Category Theory

Code:TKD
Ac.Year:2010/2011
Term:Winter
Curriculums:
ProgrammeFieldYearDuty
CSE-PHD-4DVI4-Elective
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
Faculty:Faculty of Mechanical Engineering BUT
Department:Department of Algebra and Discrete Mathematics FME 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.
Knowledge and skills required for the course:
Basic lectures of mathematics at technical universities
Learning outcomes and competences:
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.
Syllabus of lectures:

• Graphs and categories
• Algebraic structures as categories
• Constructions on categories
• Properties of objects and morphisms
• Products and sums of objects
• Natural numbers objects and deduction systems
• Functors and diagrams
• Functor categories, grammars and automata
• Natural transformations
• Limits and colimits
• Cartesian closed categories and typed lambda-calculus
• The cartesian closed category of Scott domains
Fundamental 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
Study literature:

• J. Adámek, Mathematical Structures and Categories (in Czech), SNTL, Prague, 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
Controlled instruction:
Written essay completing and defending.