**SEMINAR:
APPLIED CATEGORY THEORY**

MAT
563

Fall Semester 2018

Coordinator: Jonathan
Lorand

Meeting place and time: Y27
H12 / Mondays 15:00 - 17:00

Prerequisites: Linear Algebra
and Algebra

See the info-sheet
for the seminar.

**Organizational
IMPORTANT!**
If
you would like to participate in the seminar, please do two things:
1) write me an email, and 2) book the
module (MAT 563) on
the online platform of the University of Zurich.
The

(Note: the book is under editing until October 15; if you spot any typos, or have other comments/suggestions, please write here!)

The structure of our seminar will be designed to support an interactive and collaborative learning environment. We will all do the same weekly reading, so that we have one common set of material to discuss. Students will be asked to give a seminar presentation, as well as write short weekly reading responses in an online discussion forum. We can learn a lot through interaction with each other!

The main inspiration for designing this seminar comes from my recent participation in this online seminar and subsequent workshop in applied category theory. Recently, one of the participants Tai-Danae Bradley wrote up nice expository notes on applied category theory - have a look! Also, until the end of Summer 2018 John Baez is running an open online course in applied category theory based on the Fong-Spivak book as above. The course is being run through the forum of the Azimuth blog. It is very worthwhile to sign up to that forum and have a look at his lectures and the many discussions happening there.

Further references

A "theory" reference that I would recommend for beginning with category theory is this (freely available) book by Tom Leinster: Basic Category Theory. Among the various further texts, there is, for example, Emily Riehl's (also free) Category Theory in Context, and the classic book Categories for the Working Mathematician by Saunders MacLane.

Another book by David Spivak which is also focused on examples and applications in the sciences is based on this text: https://arxiv.org/abs/1302.6946

Each week, we will all read a portion of the book "Seven sketches in compositionality" as part of the "homework". The other part of the weekly homework is to post a short "reading response" in the online forum of the seminar, which will be hosted on GitHub (see below for more on how this will work). Finally, at each meeting of the seminar, someone will do a presentation on the reading that we did the preceding week. The idea is that everyone will have already read the material, and the speaker's job is to summarize and discuss the material that we read, give further insights, explain details, answer questions, and stimulate further discussion.

The forum will be hosted on GitHub, which is a website which will allow us to access and edit a LaTeX file (our "forum") simultaneously.

I will send a link to the forum to all seminar participants around the start of the semester. I expect that most of us will not yet be familiar with GitHub. Part of your homework for the first week of the semester is to get set up with GitHub and figure out the minimum of how this works! Don't worry, the internet is full of help (also, I will help as best I can), and I believe the effort required at the beginning is very worthwhile - GitHub is a useful tool. And you'll need it for this seminar!

The other thing you'll need is to know a very basic amount of LaTeX. Also here, don't worry: the internet is full of help, and you will not need to know much. But if you are new to LaTeX, you will need to make a certain effort. Again, worthhile: LaTeX is the common digital language for writing mathematics.

For getting set up with GitHub and LaTeX, I've posted some instructions and links in a section below the schedule.

Preliminary schedule of talks

All
page numbers and sections refer to the book "Seven sketches in
compositionality", unless otherwise noted.

Date
Speaker
Topic
17.09
*online*
GitHub and LaTeX (no physical meeting!)
24.09
*online*
Introductions on the online forum (no physical meeting!)
01.10
Marija
Sections 1.1 – 1.4: Generative effects, posets
08.10
Edona
Section 1.5: Galois connections
15.10
Marino
Sections 2.1 – 2.3: Symmetric monoidal posets, enrichment
22.10
Nicola
Sections 2.4 – 2.5: Constructions with enriched categories
29.10
Alain
Sections 3.1 – 3.3: Databases, categories, functors...
05.11
Niklas
Sections 3.4 – 3.5: Adjunction, data migration, (co)limits
12.11
Carina
Sections 4.1 – 4.3: Enriched profunctors
19.11
Marija
Sections 4.4 – 4.5: Categorification, compact closed categories
26.11
Olga
Sections 5.1 – 5.3: Props, signal flow graphs
03.12
Maryia
Section 5.4 + exta material: Graphical linear algebra (notes)
10.12
Edona + Marija
Sections 6.1 – 6.3: Colimits, hypergraph categories
17.12
Jonathan
Summary

**Getting
set up with GitHub. **

Some
important intial information (read fully before doing anything):

Every one of us will need a GitHub account. You do **NOT**
need
to pay for anything - anyone
can sign up for a *free* account. To sign up, go to
https://github.com/ and find your
way there. (Note: see also https://education.github.com/pack
).

GitHub uses so-called "repositories'': this word
bascially just means a "container" or "folder" where a bunch
of files can be stored and edited. There are respositories that are
private, and those that are public. The repository for our forum will
be private, and hosted by me (you will not have to set up any
repository). Once you are signed up with GitHub, i.e. once you have
an account at github.com, I can invite you via GitHub to be a
participant in the repository for our forum.

Let me
explain briefly how we will use GitHub to run our forum. Online, in
our repostory at github.com, there will be a LaTeX file (together
with a rendered/compiled PDF version of it, pluse some auxiliary
files which may be ignored) which we will all be able to access and
edit. For example, each week, after we have read a portion of the
book, each of you will post your short reading response in the forum
file. Further comments and discussion are also welcome. In order to
edit the forum file you will install a software application called
"GitHub Desktop" on your own personal computer which will allow
your computer to hold a copy of the forum file (and all the files in
our respository) and to synchronize this local copy with the "main"
file which is on github.com. The software GitHub Desktop can be
downloaded for free here: https://desktop.github.com/.
(Note: there are other ways to set things up, which do not involve
GitHub Desktop, but I would recommend this way as the easiest).

Once
you have a GitHub account, once you have been added by me to be a
collaborator on the forum's repository, and once you have installed
GitHub Desktop, then you can open GitHub Desktop and "clone" the
forum repository which is on github.com. This will create a copy of
the repository on your computer (you can choose where this folder is
stored). I then recommend using the tutorial inside of GitHub Desktop
which will teach you quickly the basics of how to use it. Further
information and guides can also be found on the webpages of
https://desktop.github.com/.
Basically, the workflow will be as follows: to make an edit on the
forum, you open GitHub Desktop and click the button for "syncing"
your local clone of the repository with the one online. Then you open
the LaTeX file for the forum using the LaTeX editor on your computer.
Once you are finished, compile and save your LaTeX file, and then
switch back to GitHub Desktop and "sync" you local version of the
file with the "main" file online. Now your edits will apear in
the main file and be visible to everyone else! In the rare event that
two people happen to edit the same portion of the forum document at
the same time, GitHub has a way to help resolve such a so-called
"merge conflict". I'll write instructions on how to deal with
this directly into the forum file, so you can read it there.

If
at any point questions come up that you can't figure out, please
ask me and I will try to help.

P.S. At the moment, I
don't think GitHub Desktop is available/installed on the computers
of the math instute. There seem to be other softwares installed for
using GitHub, but I do not know how they work (of course, if you know
how, you can use the terminal or the softwares installed). I will try
to find out more about this?

**Getting
set up with LaTeX**

If
you are unfamiliar with the basic idea of how LaTeX works, please
read about it first a bit in the internet, e.g. see
https://en.wikipedia.org/wiki/LaTeX

To
use LaTeX on your personal computer, there are various software
packages (also called "distributions") to choose from. If you do
not have such a software package installed already, I recommend
navigating to https://en.wikibooks.org/wiki/LaTeX/Installation.
Read the short introduction there and then, in the first subsection,
titled "Distributions", follow the links for the LaTeX
distribution package that is reommended for the operating system that
you use. I recommend using default pacakges, and not any custom
packages.

For this seminar, you will not need to learn
how to set up and format LaTeX documents, since I will already have
set up the forum file. You will need to get a rough sense of how
LaTeX works in general, and be able to write the mathematics which
you wish to use in making your comments in the forum. This can remain
fairly simple if you wish, or it can become more complicated as you
learn more LaTeX (e.g. how to draw commutative diagrams, embed an
image, etc.).

Further information and resources can be
found, for example, at https://www.latex-project.org/get/,
and on many other helpful sites throughout the web. Tutorials,
help-forums, youtube videos, etc. abound!

Note: there are
several software packages for LaTeX already installed on the math
instute computers (Texmaker, TeXworsk, TeXstudio). However, it is at
the moment not clear to me how straightforward it is to set up
syncing with GitHub on the institue computers, since I think that
GitHub Desktop is not installed.