Course details
Category Theory
TKD Acad. year 2012/2013 Winter 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
Completion
Time span
- 26 hrs lectures
Department
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 in 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.