M7150 Category Theory

Faculty of Science
Autumn 2006
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
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable
Mon 12:00–13:50 N41
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
there are 6 fields of study the course is directly associated with, display
Course objectives
The course introduces categories and shows how they make possible a unified understanding of various concepts in other fields of mathematics and computer science. There are introduced functors and natural transformations, defined products, coproducts and general limits and colimits and there is shown what they mean in particular situations. Among others, there is explained a connection of cartesian closed categories with the typed lambda-calculus. The course culminates with the theory of adjoint functors and with their connection with such disparate topics like free algebras, tensor prducts and compactifications.
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. Toposes: definition, examples
Literature
  • M.Barr, C.Wells, Category theory for computing sciences, Prentice Hall 1989
  • J.J.Adámek, Matematické struktury a kategorie, Praha 1982
Assessment methods (in Czech)
Výuka: přednáška Zkouška: ústní
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 2008, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2006, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2006/M7150