MAGIC009: Category Theory

Course details

A core MAGIC course

Semester

Autumn 2021
Monday, October 4th to Friday, December 10th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
40

Timetable

Fridays
10:05 - 10:55

Course forum

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Description

Category theory begins with the observation that the collection of mathematical objects of a given kind (groups, topological spaces, graphs, etc...) together with the appropriate mappings between them (group homomorphism, continuous function, graph morphism) is an interesting mathematical structure in its own right: a category. 

Category theory, i.e. the study of categories, provides tools that can be applied uniformly to different kinds of mathematical structures and a convenient language to relate them precisely. This course will be an introduction to category theory. The main theme will be universal properties in their various manifestations, which is one of the most important uses of category theory in mathematics. Apart from introducing specific concepts and presenting the key results, one of the goals of the module is to teach you how to reason categorically.

Prerequisites

It will be useful to have taken an undergraduate course in group theory or commutative algebra or some other abstract algebra course.

I will try to illustrate notions with examples from different areas, but you may find it useful to come up with examples from your preferred areas. 

Syllabus

  • Categories and functors. 
  • Universal arrows. 
  • Natural transformations and functor categories. 
  • Colimits. 
  • Duality and limits. 
  • Adjunctions. 
  • Preservation of limits. 
  • Presheaves and the Yoneda lemma.
  • Representables and limits
  • Kan extensions.

Lecturer

  • MR

    Prof Michael Rathjen

    University
    University of Leeds

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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