Math 9511A: Category Theory (Fall 2020)

Essential information

This is an online course!

  • Lectures: TuTh 9:30-11
  • Office hours: by appointment or on Discord
  • Instructor: Chris Kapulkin
  • Email: kkapulki (at)
  • Office: MC 116 (not that it matters...)
  • Website:
  • Prerequisites: There are no formal prerequisites for this course, but some familiarity with abstract algebra will be assumed. 


The course is delivered entirely online, via Zoom. The Zoom information is shared with students via OWL.

Students are required to attend the lectures under their full legal name and to have their webcams on. If a student is unable to do so, they must obtain prior written permission of the instructor.

Technical requirements: computer with working microphone and webcam, stable internet connection, and scanner or alternative (e.g., iPad). It is the student's responsibility to ensure that their device meets the system requirements for Zoom.

The course is delivered synchronously and not recorded. Producing and/or distributing audio/video recordings of the lectures will be considered an academic offense and handled accordingly.


The course will follow Chapters 1-5 of:

  • Riehl, Category Theory in Context, Dover Publications 2016.

The entire book is available for free download in pdf format from the author's website. Students are also welcome to consult:

  • Mac Lane, Categories for the Working Mathematician, 2nd Edition, 1978.

Course content

The topics will include:

  • categories, functors, and natural transformations;
  • representability and the Yoneda lemma;
  • limits and colimits;
  • adjoint functors;
  • monads and their algebras;
  • Kan extensions (time permitting);
  • homotopical algebra.


The final grades will be based on the following components:

  • assignments: 50%
  • midterm exam: 25%
  • final presentation: 25%


There will be five assignments, each worth 10% of the final grade. The first four will cover the textbook material and the fifth will cover the final part of the course (homotopical algebra).

Students are allowed to discuss assignment problems, but each student should write their solutions separately.


  • Assignment 1: released Sep 22, due Sep 29 at 9 AM;
  • Assignment 2: released Oct 6, due Oct 13 at 9 AM;
  • Assignment 3: released Oct 20, due Oct 27 at 9 AM;
  • Assignment 4: released Nov 10, due Nov 17 at 9 AM;
  • Assignment 5: released Dec 3, due Dec 10 at 9 AM.

Midterm Exam

There will a 90-minute midterm exam on November 12 (Thursday), 2020, from 9:30-11 AM, covering the textbook material (i.e., excluding the final part of the course).

Final Presentation

During the final examination period of the course, each student will be required to give a 30-minute presentation. The instructor will prepare a list of potential topics, but the students are welcome, and in fact encouraged, to suggest their own topic. The topic of the presentation must be a meaningful application of categorical methods to any area of mathematics, computer science, physics, or philosophy that is approved by the instructor. The instructor is reasonable. (-:

Accommodation and Accesibility

If you are unable to meet a course requirement due to illness or other serious circumstances, you must provide valid medical or supporting documentation to the Academic Counselling Office of your home faculty as soon as possible. If you are a Science student, the Academic Counselling Office of the Faculty of Science is located in WSC 140, and can be contacted at

For further information, please consult the university’s medical illness policy at

If you miss the Final Exam, please contact your faculty’s Academic Counselling Office as soon as you are able to do so. They will assess your eligibility to write the Special Exam (the name given by the university to a makeup Final Exam). You may also be eligible to write the Special Exam if you are in a “Multiple Exam Situation”

Academic Policies

The website for Registrarial Services is

In accordance with policy, centrally administered e-mail account provided to students will be considered the individual’s official university e-mail address. It is the responsibility of the account holder to ensure that e-mail received from the University at his/her official university address is attended to in a timely manner.


Scholastic offences are taken seriously and students are directed to read the appropriate policy, specifically, the definition of what constitutes a Scholastic Offence, at this website:

Student Accessibility Services

Western is committed to achieving barrier-free accessibility for all its members, including graduate students. As part of this commitment, Western provides a variety of services devoted to promoting, advocating, and accommodating persons with disabilities in their respective graduate program.

Graduate students with disabilities (for example, chronic illnesses, mental health conditions, mobility impairments) are encouraged to register with Student Accessibility Services, a confidential service designed to support graduate and undergraduate students through their academic program. With the appropriate documentation, the student will work with both SAS and their graduate programs (normally their Graduate Chair and/or Course instructor) to ensure that appropriate academic accommodations to program requirements are arranged.  These accommodations include individual counselling, alternative formatted literature, accessible campus transportation, learning strategy instruction, writing exams and assistive technology instruction.