M7150 Category Theory

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 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
Prerequisites
Knowledge of basic algebraic concepts is welcome.
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 and its significance for mathematics. At the end of the course a student: understands basic categorical concepts; masters the categorical way of thinking; is able to analyze categorical context of mathematical concepts and results; is aware of possibilities of a conceptual approach to mathematics.
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
Teaching methods
The course: presents required knowledge and ways of thinking; shows their applications; stimulates a discussion about its subject.
Assessment methods
Course ends by an oral exam. Presence at the course recommended. Homeworks are given but not controled.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Spring 2001, Autumn 2002, Autumn 2004, Autumn 2006, Autumn 2008, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020, Autumn 2022, Autumn 2024.