M027 Category Theory

Faculty of Informatics
Spring 2001
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments – Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Prerequisites
M005 Foundations of mathematics && M003 Linear Algebra and Geometry I && M004 Linear Algebra and Geometry II && M008 Algebra I && M009 Algebra II
Before enrolling this course the students should go through M005 Foundations of mathematics, M003 Linear Algebra and Geometry I, M004 Linear Algebra and Geometry II, M008 Algebra I, M009 Algebra II, M006 Set Theory and M007 Mathematical Logic.
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
Syllabus
  • Categories: category, constructions of categories, special objects and morphisms
  • Products and sums
  • Functors: functor, diagram
  • Natural transformations: natural transformation, Yoneda lemma, representable functors
  • Cartesian closed categories
  • Limits: equalizer, pullback, limit, colimit, limits by products and equalizers
  • Adjoint functors: adjoint functor, Freyd's theorem
  • Closed categories: monoidal category, symmetric monoidal closed category, connection with linear logic
Literature
  • BARR, Michael and Charles WELLS. Category theory for computing science. 2nd ed. London: Prentice-Hall, 1995, xvii, 325. ISBN 0-13-323809-1. info
  • ADÁMEK, Jiří. Matematické struktury a kategorie. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1982, 269 s. URL info
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Autumn 1996, Autumn 1998.
  • Enrolment Statistics (recent)
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