Faculty of Information Technology, BUT

Course details

Category Theory

TKD Acad. year 2009/2010 Summer semester

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

Language of instruction

Czech

Completion

Examination (written)

Time span

39 hrs lectures

Assessment points

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 kwnowledge and skills

Basic lectures of mathematics at technical universities

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

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

Controlled instruction

Written essay completing and defending.

Course inclusion in study plans

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