Course details

Category Theory

TKD Acad. year 2006/2007 Summer semester

Current academic year

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.

Guarantor

Šlapal Josef, prof. RNDr., CSc. (IM DAAG)

Language of instruction

Czech, English

Completion

Examination

Time span

  • 39 hrs lectures

Department

Faculty of Information Technology (FIT)

Subject specific learning outcomes and competences

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.

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.

Prerequisite knowledge and skills

Basic lectures of mathematics at technical universities

Study literature

  • 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

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

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
  • Adjoint functors
  • Cartesian closed categories and typed lambda-calculus
  • The cartesian closed category of Scott domains

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

Written essay completing and defending.

Back to top