M7170 Reading seminar from category theory

Faculty of Science
Autumn 2022
Extent and Intensity
0/1/0. 1 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
Teacher(s)
doc. John Denis Bourke, PhD (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
Thu 11:00–11:50 MS1,01016
Prerequisites
M2150 Algebra I || M2155 Algebra 1 || ( FI:MB008 Algebra I ) || PROGRAM(N-MA) || PROGRAM(1433:N-IN)
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.
The capacity limit for the course is 16 student(s).
Current registration and enrolment status: enrolled: 3/16, only registered: 0/16, only registered with preference (fields directly associated with the programme): 0/16
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 seminar will (tentatively) involve papers and textbooks covering several themes:
  • 1) Grothendieck fibrations and bifibrations;
  • 2) Cauchy-completeness for enriched categories, generalising cauchy-completeness for metric spaces;
  • 3) Relative monads and skew monoidal categories;
  • 4) Arithmetic universes and Godel's incompleteness theorem;
  • 5) The effective topos.
  • The list of associated papers, to be updated, is
  • 1) TBA
  • 2) Lawvere: Metric spaces, generalized logic and closed categories.
  • 3) Altenkirch et al: Monads need not be endofunctors.
  • 4) van dijk et al: Godel's theorem after Joyal.
  • 5) Hyland: The effective topos.
Teaching methods
The plan is that this will be a live seminar, though could be in hybrid form with some talks online.
Assessment methods
Evaluation of an activity.
Language of instruction
English
Further Comments
Study Materials
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, Spring 2021, autumn 2021, Spring 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/M7170