Class Information

Course Title Math 477T: Category Theory

Instructor Julia Kameryn Williams

Website http://kamerynjw.net/teaching/2024/math477t/

Email kwilliams [at] simons-rock (dot) edu

Primary out of class contact course website or email me

Tutorial Hours and Room

  • T 1:00–2:00, F 3:45–4:45

  • Math tutorial room

Office Hours M 3:45–4:45, WF 2:35–3:35

Office 2T Hall College Center

Textbook Emily Riehl, Category Theory in Context (2016).

Course Description Category theory is a branch of mathematics which has been described as the mathematical study of analogies of analogies. In this tutorial we will learn the basic notions of the field, including functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, and Kan extensions. We will also look at applications of category theory to other areas of mathematics.

Prerequisite Instructor permission.

Learning Outcomes

This tutorial is an introduction to category theory. After taking it you should be able to analyze commutative diagrams, prove category theoretic statements, and understand how category theory connects to other branches of mathematics.

Grading Policy

As a tutorial this will be driven by you, the students. If you are putting forth the necessary effort to make this tutorial a success, then you are putting forth the necessary effort to get an A. Specifically, you will be graded on your contribution to the lecture. Your contribution will be assessed by your weekly presentations and your submission of your lecture notes at the end of the semester. Here are the grading specifications.

  • A. Participate fully. Present your share of the material from the book, actively listen to others’ presentations, and solve exercises from the text. Submit your lecture notes to the instructor at the end of the semester.

  • C. Start off participating fully but fall off. You have to cancel a few presentations, putting the tutorial behind. Or you don’t engage when you’re not presenting.

  • F. Don’t meaningfully participate.

I reserve the use of B’s and D’s for borderline cases.

Class Structure

The tutorial will be structured as a reading group. We will read through the text together, and the students will take turns presenting material.

Student Responsibilities

You are the ones who make the tutorial happen. Unlike a class, more of the work here falls on your shoulders. In particular, you are responsible for the lecture portion of the class.

There are two students in the tutorial and we meet twice a week. Each week you will give one of the two lectures. We will progress through the textbook, with your lectures covering the material therein. Your lectures should include both the main contents of the book as well as some of the exercises. Treat this like you are teaching a class, because you are. You should write clearly on the blackboard, giving full statements of definitions and theorems. Your work should be understandable to the audience, and you should be able to respond to questions from your classmates. When you are in the audience, you should listen attentively and take notes. Ask questions, contribute suggestions to arguments, and generally be respectful and supportive to your fellow classmates.

You should keep your lecture notes in one place. You will submit them to me at the end of the semester.

Instructor Responsibilities

I will read the text with you and attend meetings. I will be available as a resource both during class meetings and outside of class.

Textbook Information

Emily Riehl, Category Theory in Context, Dover Press (2016). ISBN: 978-0486809038.

Accessibility

Students with disabilities are legally entitled to reasonable accommodations to ensure equal access to education. I am committed to providing you with equal access to this class, and am happy to work with you to ensure reasonable accommodations. Because the accommodations offered are usually forward-looking modifications, it is important to get them set up as soon as possible.

Anyone who feels they may need accommodation based on the impact of a disability should contact Jeannie Altshuler, Director of Accessibility and Academic Support, in the Win Commons (jaltshuler@simons-rock.edu; 413-528-7383).

The Americans with Disabilities Act defines a disability as a medical condition that substantially limits one or more major life activities—including things like walking, sleeping, taking care of yourself, learning, and regulating your emotions—or major bodily functions. If you have a medical condition—including mental health conditions—that significantly interferes with your schoolwork, you probably qualify. You do not need to disclose your condition to your instructors to receive accommodations.

Academic Honesty

You are expected to know and uphold the college’s policies on academic honesty as described in the Student Handbook. Mathematics classes form part of the core base of skills you need to succeed in many later classes, and you are harming yourself if you try to avoid learning the material for this class.

The use of ChatGPT or other AI tools is prohibited, and will count as a failure to participate.

You are encouraged to collaborate with classmates for homework, but the work you submit is expected to be your own. If you do work with others, please say so and give their names with your submitted homework.

Other Campus Resources

The Wellness Center Health and Counseling Services, as the name says, offers health and counseling services.

The Win Student Resources Commons offers academic support, tutoring, accessibility, and career advice.

Tentative Schedule

  • August 27. Logistics meeting.

  • August 29. Preparation time. No meeting.

  • September 3. Sections 1.1 and 1.2.

  • September 6. Sections 1.3 and 1.4.

  • September 10. Sections 1.5, 1.6, and 1.7.

  • September 13. Sections 2.1 and 2.2.

  • September 17. Sections 2.3 and 2.4.

  • September 20. Sections 3.1, 3.2, and 3.3.

  • September 24. Sections 3.4, 3.5, 3.6.

  • September 27. Sections 3.7 and 3.8.

  • October 1 and 4. Break!

  • October 8. Sections 4.1 and 4.2.

  • October 11. Sections 4.3 and 4.4.

  • October 15. Sections 4.5 and 4.6.

  • October 18. Sections 5.1, 5.2, and 5.3.

  • October 22. Sections 5.4 and 5.5.

  • October 25. Sections 5.6.

  • October 29. Sections 6.1.

  • November 1. Sections 6.2.

  • November 5. Sections 6.3.

  • November 8. Sections 6.4 and 6.5.

  • Remainder. Epilogue, and extra time for when it turns out the tentative schedule was too ambitious.

Notice of Changes

This syllabus is subject to change. If this happens, you will be informed of any additions or changes.