Course detail

Category Theory

FIT-TKDAcad. year: 2010/2011

Not applicable.

Language of instruction

Czech

Number of ECTS credits

0

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Šlapal, CSc.

Department

Dept. of Algebra and Discrete Mathematics (ÚM OAAG)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Not applicable.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Not applicable.

Specification of controlled education, way of implementation and compensation for absences

Not applicable.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic 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

Recommended reading

  • 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

Classification of course in study plans

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, winter semester, elective

  • Programme VTI-DR-4 Doctoral

    branch DVI4 , any year of study, winter semester, elective

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. RNDr. Josef Šlapal, CSc.

Syllabus

  • 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