Announcements


At the end of lecture 8 you'll now find a proof of the Adjoint Functor Theorem. I also added examples of non-representable functors to lecture 10.

Forum

General


This course is part of the MAGIC core.

Description

Category theory is the language of much of modern mathematics. It starts from the observation that the collection of all mathematical structures of a certain kind may itself be viewed as a mathematical object - a category.

This is an introductory course in category theory. The main theme will be universal properties in their various manifestations, one of the most important uses of categories in mathematics.

Semester

Spring 2017 (Monday, January 23 to Friday, March 31)

Timetable

  • Thu 14:05 - 14:55

Prerequisites

Category theory is an abstract algebraic point of view of mathematics. Some familiarity with an algebraic way of thinking is important. It is therefore an advantage to have studied an undergraduate course in group theory or ring theory, or some other abstract algebra course. I will assume some knowledge of algebra such as vector spaces and their bases, and groups, but a basic undergraduate level knowledge of these subjects is sufficient.

Syllabus

The topics covered are:
  1. Categories
  2. Functors and natural transformations
  3. Adjoints
  4. Limits
  5. Colimits
  6. Interaction between limits and adjoints
  7. Adjoint functor theorems
  8. Representables
  9. Presheaves and the Yoneda lemma
  10. Representables and limits

Lecturer


Michael Rathjen
Email M.Rathjen@leeds.ac.uk
Phone +44 (0)113 3435109
vcard


Students


Photo of Mashaer Alsaeedi
Mashaer Alsaeedi
(Birmingham)
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Floriana Amicone
(Manchester)
Photo of Michael Arnold
Michael Arnold
(East Anglia)
Photo of Thomas Baker
Thomas Baker
(*Ext_Assessed)
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Carolyn Barker
(Leeds)
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Edward Bennett
(Nottingham)
Photo of John Blackman
John Blackman
(Durham)
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Philip Carter
(Liverpool)
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Lucas Das Dores
(Liverpool)
Photo of Lorenzo De Biase
Lorenzo De Biase
(Cardiff)
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Liam Dobson
(Newcastle)
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Paul Druce
(Nottingham)
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Aeran Fleming
(Liverpool)
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Dominic Foord
(Liverpool)
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Christopher Foster
(Manchester)
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Ai Guan
(Lancaster)
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Ben Jones
(Cardiff)
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Vijay Joshi
(Birmingham)
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Ulla Karhumäki
(Manchester)
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Zoltan Kocsis
(Manchester)
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Rosario Mennuni
(Leeds)
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George Morrison
(Sussex)
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Andrea Pachera
(Birmingham)
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Wojciech Porowski
(Nottingham)
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Matthew Poulter
(Lancaster)
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Christopher Seaman
(Cardiff)
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Daria Shschedrina
(Nottingham)
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Giulia Sindoni
(Leeds)
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Anna Szumowicz
(Durham)
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Fabio Tanania
(Nottingham)
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Matty Van Son
(Liverpool)
Photo of Albert Wood
Albert Wood
(*External)


Bibliography


Categories for the working mathematicianMac Lane
Basic Category TheoryLeinster


Note:

Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)

Assessment



The assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be 4 questions. Each question will be marked out of 20. To pass the exam you will need ≥ 40 points out of the total of 80 points.

Exam category theory 2017

Files:Exam paper
Released: Monday 24 April 2017 (63.4 days ago)
Deadline: Sunday 7 May 2017 (49.4 days ago)


Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-15ct-lecture1_handout.pdfL
1-15ctlecture2_handout.pdfL
1-15ctlecture3_handout.pdfL
1-15ctlecture4_handout.pdfL
1-15ctlecture5_handout.pdfL
1-15ctlecture6_handout.pdfL
1-15ctlecture7-handout.pdfL
1-15ctlecture8.pdfL
1-15ctlecture9.pdfL
1-15ctlectures10.pdfL


Recorded Lectures


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