M7170 Reading seminar from category theory

Faculty of Science
Spring 2021
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)
prof. RNDr. Jiří Rosický, DrSc. (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
Timetable of Seminar Groups
M7170/01: No timetable has been entered into IS. J. Rosický
Prerequisites
Graduation of M7150 Category theory.
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
  • Mathematics (programme PřF, M-MA, specialization Discrete Mathematics)
  • Mathematics (programme PřF, N-MA, specialization Discrete Mathematics)
Course objectives
An ability to understand and present research papers in category theory including a survey of related literature.
Learning outcomes
Mastering of given special areas of category theory. A preparation for an independent research work in this area.
Syllabus
  • The study of:
  • M. Hyland and J. Power, The category theoretic understanding of universal algebra: Lawvere theories and monads.
  • G. M. Kelly, Elementary observations on 2-categorical limits.
  • R. Garner, An embedding theorem for tangent categories.
Literature
  • M. Hyland and J. Power, The category theoretic understanding of universal algebra: Lawvere theories and monads, El. Notes in Th. Comp. Sci. 172 (2007), 437-458.
  • R. Garner, An embedding theorem for tangent categories, Adv. Math. 323 (2018), 668-687
  • G. M. Kelly, Elementary observations on 2-categorical limits, Bull. Austral. Math. Soc. 39 (1989), 301-317.
Teaching methods
Student's on-line reports with a discussion.
Assessment methods
Evaluation of an activity.
Language of instruction
English
Further comments (probably available only in Czech)
Study Materials
The course is taught only once.
Teacher's information
A study of three directions in category theory:

Lawvere theories an monads with an applications to theoretical compuer science.

Basics of 2-category theory.

Categories equipped with tangent functor motivated by diffrerntial geometry.

The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2001, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Spring 2019, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025.
  • Enrolment Statistics (Spring 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2021/M7170