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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Category Theory (MATH11237)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryA first course in category theory, covering the basic concepts of the subject and their relevance to other parts of mathematics

First course in category theory covering the following topics:
- Categories, functors and natural transformations
- Universal properties
- Adjunctions, limits and representability
- Uses of categorical concepts in other parts of mathematics
Course description Category theory begins with the observation that the collection of all mathematical structures of a given type, together with all the maps between them, is itself a nontrivial structure which can be studied in its own right. Since the birth of category theory in the 1940s, this mild observation has had great success in unifying and systematizing broad swathes of mathematics. It has now become an indispensable tool in algebra, topology and geometry, and its applications even reach into parts of computer science, physics and other branches of science.

Category theory provides a bird's eye view of mathematics, revealing patterns that are invisible from ground level. But it is not all about big concepts: as for any other subject, learning category theory involves acquiring some technical skills. Central to this course is the notion of universal property, made precise through the related concepts of adjoint functors, limits and representability. Students taking this course will learn both the relevance of category theory to other parts of mathematics and a rigorous body of definitions, theorems and proofs.


1. Categories, functors and natural transformations
2. Adjoints
3. Representables
4. Limits
5. Adjoints, representables and limits
6. (Optional) Further topics in category theory (e.g. abelian categories, toposes, monads, enriched categories, monoidal categories)
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Algebra (MATH10069)
Prohibited Combinations Other requirements The course will feature many examples drawn from algebra and topology. Although it is not essential to understand all of these examples, students who have taken some Level 10/11 courses in algebra (e.g. MATH10079 Group Theory) or topology (e.g. MATH10076 General Topology) will be at an advantage.
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Work with the core concepts of category theory and give examples of how they appear in other parts of mathematics.
  2. Understand and explain the relationship between adjointness, limits and representability.
  3. Work with theorems in category theory, explain key steps in proofs, and summarize proofs.
  4. Solve unseen problems in category theory, giving arguments at an appropriate level of detail.
Reading List
Tom Leinster, Basic Category Theory. Cambridge University Press, 2014.
Emily Riehl, Category Theory in Context. Dover, 2016.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsCatTH,Category Theory,Foundations
Course organiserDr Thomas Leinster
Tel: (0131 6)50 5057
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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