Course details
Category Theory
TKD Acad. year 2013/2014 Winter semester
Small and large categories, algebraic structures as categories, constructions on categories (free categories, subcategories and dual categories), special types of objects and morphisms, products and sums of objects, categories with products and circuits, categories with sums and flow charts, distributive categories and imperative programs, data types (arithmetics of reals, stacks, arrays, Binary trees, queues pointers, Turing Machines), functors anf functor categories, directed graphs and regular grammars.
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 oriented on applications in computer science. Individual categorical concepts and results are discussed from the view point of their meaning and use in computer science.
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.
Teaching methods and criteria
The course uses teaching methods in form of Lecture - 2 teaching hours per week.
Controlled instruction
Written essay completing and defending.
Course inclusion in study plans