M7151 Exersices in Category Theory

Faculty of Science
Autumn 2023

The course is not taught in Autumn 2023

Extent and Intensity
0/2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
Teacher(s)
Giulio Lo Monaco, Ph.D., M.Sc. (lecturer)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: 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 introduction of basic category theory and its significance for mathematics is supported.
Learning outcomes
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
  • AWODEY, Steve. Category theory. 2nd ed. New York [N.Y.]: Oxford University Press, 2010, xv, 311. ISBN 9780199237180. info
Teaching methods
Complements required knowledge and ways of thinking; shows their applications; stimulates a discussion about its subject.
Assessment methods
Ends with credit. Presence obligatory. Homeworks are given and controled.
Language of instruction
English
Further Comments
Course is no more offered.
The course is taught: every week.
The course is also listed under the following terms Autumn 2014, Autumn 2016, Autumn 2018.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/M7151