Course detail
Category Theory
FIT-TKDAcad. year: 2021/2022
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.
Language of instruction
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Learning outcomes of the course unit
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Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
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Aims
Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
Recommended reading
J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982
M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
S. Roman, Introduction to Language of Category Theory, Birkhauser Verlag AG, 2017
Classification of course in study plans
- Programme DIT Doctoral 0 year of study, summer semester, compulsory-optional
- Programme DIT Doctoral 0 year of study, summer semester, compulsory-optional
- Programme CSE-PHD-4 Doctoral
branch DVI4 , 0 year of study, summer semester, elective
- Programme CSE-PHD-4 Doctoral
branch DVI4 , 0 year of study, summer semester, elective
- Programme DIT-EN Doctoral 0 year of study, summer semester, compulsory-optional
- Programme DIT-EN Doctoral 0 year of study, summer semester, compulsory-optional
- Programme CSE-PHD-4 Doctoral
branch DVI4 , 0 year of study, summer semester, elective
- Programme CSE-PHD-4 Doctoral
branch DVI4 , 0 year of study, summer semester, elective
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Small and large categories
- Algebraic structures as categories
- Constructions on categories
- Properties of objects and morphisms
- products and sums of objects
- Categories with products and circuits
- Categories with sums and flow charts
- Distributive categories
- Imperative programs
- Data types stack, array and binyry tree
- Data types queue and pointer, Turing machines
- Functors anf functir categories
- Grammars and automata
Guided consultation in combined form of studies
Teacher / Lecturer