# Category Theory Lecture series from Steven Roman

Steven Roman has a series of six lectures on category theory from 2015:

# Dr. Martin Codrington’s “Category Theory: The Beginner’s Introduction”

Dr. Martin Codrington just uploaded an excellent-looking set of videos to YouTube:

# Online Video Conference Meetings

Now that we’re a few days into the group and most everyone seems to be registered and has had some time to respond to the initial questionnaire, I thought I’d set a time for our online meeting(s)/sessions.

Most people have indicated to me that they’ve either already bought/received the text and have started reading, or are about to begin. I have a feeling  that most will find the first several chapters very basic, (but we’re all here to help those that don’t).

There are currently 25 people registered!

As a reminder, as mathematically “sophisticated” readers, we’ll be using a “flipped” format for our meetings, so everyone will generally be expected to have read the appropriate sections and worked on some problems/examples ahead of the meetings so that they can bring any problems/issues they may have to get some help from the rest of the group.

## Upcoming meetings

As an initial meeting, let’s aim for:

Friday, June 5, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

In this session, we can get any  basic administrative things out of the way and discuss any problems/issues anyone may have with the first two chapters which primarily cover some initial basics including set theory and functions.

For our regular, weekly standing meetings, let’s shoot for

Monday evenings at 6:45pm Pacific / 9:45 pm Eastern.

Hopefully this weekly time will work for those on both coasts of the Americas without any undue burden.  We can attempt to record sessions for those who aren’t able to make it due to time zone or other conflicts, but no one seemed to have any issues with Mondays and we seem to be roughly split with participants on both coasts.

The second meeting will be on:

Monday, June 8, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

We’ll cover everyone’s questions from the following sections (which everyone will have been expected to have read beforehand):

2.3 Ologs; 3.1 Products and coproducts; and 3.2 Finite limits in Set

If necessary, outside of this, we can try to hold an alternate time on Saturday, which was the other day no one seemed to have issues with. An earlier time may help those who live outside the Americas as well. Anyone who’d like an alternate time is invited to mention it in the comments below.

Due to platform requirements and the diversity of the participants, Google Hangouts seems to work for everyone and allows video, audio, screensharing, and most of the other useful features we might want.  As I recall, one doesn’t necessarily need a Google+ account, but can login through their gmail interface (typically with a browser plugin), or via the hangout app on the bigger cell phone platforms.

You can click on the individual links for the appropriate date to find/join the particular hangout on this page (above), or on the individual links listed within the syllabus.

## Office Hours

As a reminder, most participants have indicated office hours during which they are available to chat with others to offer assistance or help. I’d hope that everyone would try to login to Google Hangouts and make themselves relatively available to others to offer assistance, if they’re able during their stated office hours. Remember that helping others can assist you in reviewing/clarifying the material for yourself as well.

As always, additional assistance can also be easily had by making a post here to the “blog” with a specific question or problem and everyone can take a stab at helping out through the comments on that particular post.

If you haven’t already done so, feel free to do the following:

We all look forward to seeing you soon!

# How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

For those who are intimidated by the thought of higher mathematics, but are still considering joining our Category Theory Summer Study Group, I’ve just come across a lovely new book by Eugenia Cheng entitled How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics.

It just came out in the U.S. market on May 5, 2015, so it’s very new in the market. My guess is that even those who aren’t intimidated will get a lot out of it as well. A brief description of the book follows:

“What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.

At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.”

Dr. Cheng recently appeared on NPR’s Science Friday with Ira Flatow to discuss her book.  You can listen to the interview below. Most of the interview is about her new book. Specific discussion of category theory begins about 14 minutes into the conversation.

Dr. Eugenia Cheng can be followed on Twitter @DrEugeniaCheng. References to her new book as well as some of her syllabi and writings on category theory have been added to our resources pages for download/reading.

# Twitter List of Category Theory Participants

The link below is for a twitter list of all the participants in the study group, (or at least all those I’m aware of presently who have twitter accounts). One can subscribe to the list or individually follow each of those on it as one wishes.

Twitter list of participants in the category theory study group

A Twitter list help page is available for those who need it.

# Commutative Diagrams in LaTeX

## Overview

With my studies in category theory trundling along, I thought I’d take  moment to share some general resources for typesetting commutative diagrams in $\LaTeX$. I’ll outline below some of the better resources and recommendations I’ve found, most by much more dedicated and serious users than I. Following that I’ll list a few resources, articles, and writings on some of the more common packages that I’ve seen mentioned.

Naturally, just reading through some of the 20+ page user guides to some of these packages can be quite daunting, much less wading through the sheer number that exist.  Hopefully this one-stop-shop meta-overview will help others save some time trying to figure out what they’re looking for.

### Feruglio Summary

Gabriel Valiente Feruglio has a nice overview article naming all the primary packages with some compare/contrast information. One will notice it was from 1994, however, and misses a few of the more modern packages including TikZ. His list includes: AMS; Barr (diagxy); Borceux; Gurari; Reynolds; Rose (XY-pic); Smith (Arrow); Spivak; Svensson (kuvio); Taylor (diagrams); and Van Zandt (PSTricks). He lists them alphabetically and gives brief overviews of some of the functionality of each.

Feruglio, Gabriel Valiente. Typesetting Commutative Diagrams.  TUGboat, Volume 15 (1994), No. 4

### Milne Summary

J.S. Milne has a fantastic one-page quick overview description of several available packages with some very good practical advise to users depending on the level of their needs. He also provides a nice list of eight of the most commonly used packages including: array (LaTeX); amscd (AMS); DCpic (Quaresma); diagrams (Taylor); kuvio (Svensson); tikz (Tantau); xymatrix (Rose); and diagxy (Barr). It’s far less formal than Feruglio, but is also much more modern. I also found it a bit more helpful for trying to narrow down one or more packages with which to play around.

Milne, J.S. Guide to Commutative Diagram Packages.

### Spivak Pseudo-recommendations

David Spivak, the author of Category Theory for the Sciences, seems to prefer XY-pic, diagXY, and TikZ based on his website from which he links to guides to each of these.

## Resources for some of the “Bigger” Packages

Based on the recommendations given in several of the resources above, I’ve narrowed the field a bit to some of the better sounding packages. I’ve provided links to the packages with some of the literature supporting them.