#
PřF:M7150 Category Theory - Course Information

## M7150 Category Theory

**Faculty of Science**

Autumn 2020

**Extent and Intensity**- 2/2/0. 6 credit(s). Type of Completion: zk (examination).

Taught partially online. **Teacher(s)**- prof. RNDr. Jiří Rosický, DrSc. (lecturer)

Giulio Lo Monaco, M.Sc. (seminar tutor) **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 **Timetable**- Mon 12:00–13:50 M3,01023
- Timetable of Seminar Groups:

*G. Lo Monaco* **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**- Algebra and Discrete Mathematics (programme PřF, N-MA)
- Applied Informatics (programme FI, N-AP)
- Geometry (programme PřF, N-MA)
- Logics (programme PřF, N-MA)

**Course objectives**- The course introduces basic category theory and its significance for mathematics.
**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*. 1st. pub. Oxford: Clarendon Press, 2006. xi, 256. ISBN 0198568614. info

*required literature*- Leinster, Basic Category Theory, https://arxiv.org/pdf/1612.09375.pdf
- S. Abramsky, Introduction to categories and categorical logic, https://www.academia.edu/2781769/Introduction_to_categories_and_categorical_logic?auto=download&email_work_card=download-paper
- E. Riehl, Category theory in context, Dover Publ. 2017, https://web.math.rochester.edu/people/faculty/doug/otherpapers/Riehl-CTC.pdf

*recommended literature*- J.J.Adámek, Matematické struktury a kategorie, Praha 1982
- BARR, Michael and Charles WELLS.
*Category theory for computing science*. 2nd ed. London: Prentice-Hall, 1995. xvii, 325. ISBN 0-13-323809-1. info

*not specified*- AWODEY, Steve.
**Teaching methods**- The on-line course: presents required knowledge and ways of thinking; shows their applications; stimulates a discussion about
its subject.

Exercises: solving theoretical problems focused on practising basic concepts and theorems. **Assessment methods**- Course ends by an oral exam. Presence at the course recommended. Homeworks are given, handed in exercises.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2020/M7150