M7150 Category Theory

Faculty of Science
Autumn 2008
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 10:00–11:50 M5,01013
Prerequisites
Monoids, ordered sets.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course introduces basic category theory. Presented concepts and their properties are illustrated by numerous examples from mathematics, logic and computer science. The goal is to learn a categorial way of thinking and its use in concrete situations. This makes students able to recognize an abstract pattern of seemingly distinct concepts, constructions and results.
Syllabus
  • 1. Categories: definition, examples, constructions of categories, special objects and morphisms 2. Products and coproducts: definition, examples 3. Funtors: definition, examples, diagrams 4. Natural transformations: definition, examples, Yoneda lemma, representable functors 5. Cartesian closed categories: definition, examples, connections with the typed lambda-calculus 6. Limits: (co)equalizers, pullbacks, pushouts, limits, colimits, limits by products and equalizers 7. Adjoint functors: definition, examples, Freyd's theorem 8. Monoidal categories: definition, examples, connections with linear logic, enriched categories
Literature
  • J.J.Adámek, Matematické struktury a kategorie, Praha 1982
  • AWODEY, Steve. Category theory. 1st. pub. Oxford: Clarendon Press, 2006, xi, 256. ISBN 0198568614. info
  • BARR, Michael and Charles WELLS. Category theory for computing science. 2nd ed. London: Prentice-Hall, 1995, xvii, 325. ISBN 0-13-323809-1. info
Assessment methods
Lectures: presence recommended, homeworks given, not controled Exams: oral
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Spring 2001, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2008, recent)
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