MM857: Introduction to category theory
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310060102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master
STADS ID (UVA): N310060101
ECTS value: 5
Date of Approval: 05-10-2022
Duration: 1 semester
Version: Approved - active
Comment
Entry requirements
Academic preconditions
Academic preconditions. Students taking the course are expected to have a basic knowledge of algebra, corresponding to the contents of the courses MM505/MM568 and MM551/MM567.
Course introduction
The aim of the course is to introduce the student to category theory, which is a formalization of mathematical structure. Category theory has, a part from its mathematical relevance, applications in computer science (programming language theory).
The course primarily builds on the knowledge acquired in the courses MM505 (Linear algebra) and MM551 (Algebra 1). The course gives the student a deeper insight into the similarities between different mathematical structures.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to take responsibility for the academic development and specialization.
- Give the competence to develop an overview of the interplay between different mathematical disciplines.
- Give the competence to switch fluently between abstract theory and concrete mathematical examples and understand the interaction between abstract theory and concrete problems.
- Give skills to work concretely with new mathematical tools and objects.
- Give skills to learn and understand advanced mathematical theories at a more independent level.
- Give knowledge and understanding of category theory as exemplified by different parts of mathematical theory (primarily algebra).
- Bring perspective into the student’s mathematical knowledge.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- Reproduce definitions and results, including their proofs, covered in the course.
- Be able to use these results to analyze concrete examples.
- Formulate and present definitions, proofs and calculations in a mathematically rigorous way.
- Master complex proofs within the curriculum.
- Independently construct proofs within category theory.
Content
The following main topics are contained in the course: A selection of the 5 main concepts in category theory:
- categories
- functors
- natural transformations
- universality
- adjunction
Literature
Examination regulations
Exam element a)
Timing
June
Tests
Oral examination
EKA
N310060102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card
Language
Normally, the same as teaching language
Duration
30 minutes
Examination aids
To be announced during the course
ECTS value
5
Indicative number of lessons
Teaching Method
The teaching method is based on three phase model.
- Intro phase: 28 hours
- Skills training phase: 14 hours, hereof tutorials: 14 hours
Activities during the study phase:
- Solution of weekly assignments in order to discuss these in the exercise sections
- The students are expected to familiarize themselves with the material covered in the lectures
- Self study of various parts of the course material
- Reflection upon the intro and training sections
Teacher responsible
Additional teachers
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.