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Please note that you'll find exercises at the end of most of the uploaded weekly course "handouts". Needless to say, they are very useful for comprehending the material.

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


Bibliography


Categories for the working mathematicianMac Lane
Basic Category TheoryLeinster


Note:

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Assessment



No assessment information is available yet.

No assignments have been set for this course.

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


Recorded Lectures


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