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Category Theory Search Primary Menu About Syllabus Course Resources Textbooks Videos Open Course Ware Alternate Syllabi Course Notes / Online Texts Popular Science Books & Texts for the Non-specialist Participants Participant Registration Login Join Subscribe Blog Introdution (Chapter 1) Category of Sets (Chapter 2) Fundamental Considerations in Set (Chapter 3) Categories and Functors (Chapter 4) Basic Category Theory (Chapter 5) Fundamental Considerations of Categories (Chapter 6) Categories at Work (Chapter 7) Search for: Categories and Functors (Chapter 4) Week Six Meeting: §4.3 Category Theory , Resources How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics Category Theory , Resources Commutative Diagrams in LaTeX Administrative , Category Theory The Category Theory Site Is Now Live Administrative , Category Theory Category Theory Summer Study Group 2015 Administrative , Category Theory Category Theory Anyone? About Welcome to the Category Theory Study Group! For over 30 years Professor Michael Miller has been teaching advanced mathematics courses through UCLA’s Extension program. He’s built up a following of 20-30 regulars” who are always augmented by several welcome newcomers. As a camaraderie has built up among the participants over the years (and because Mike only teaches in the Fall and Winter quarters) many of his regular students choose a subject or two to study as a group throughout the Spring or Summer months. (Past groups have delved into Lie Groups, Quantum Mechanics, and Algebraic Geometry among others.) This year a group of us has settled on the vibrantly growing field of category theory and we invite you to join us. Exercise Your Brain Whether you’re a professional mathematician, engineer, physicist, physician, high schooler, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of this study group, not to mention the camaraderie of others including some of the regulars” from Dr. Miller’s classes who all have widely varying backgrounds (literally from actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years. Only a very few in the group have dabbled directly in the subject area in the past, but there’s enough depth and diversity in the group already that we should be able to get fairly far into the subject by ourselves. Beginners Welcome! Even if it’s been years since you last took Calculus or Linear Algebra, we will all help you get quickly back up to speed in studying mathematics. (One should note that the text we’ve chosen doesn’t have any significant prerequisites, though at least a passing knowledge of high school set theory might help.) If you’re interested in mathematics, physics, computer science, programming, quantum mechanics, quantum information, or even string theory, this is one of the topics that is rapidly becoming de rigueur for delving in deeply and being able to understand them better. And naturally, it’s simply a beautiful and elegant subject for those who have no need to apply it to anything, but who just want to meander their way through higher mathematics for the fun of it (this will probably comprise the largest majority of the group by the way.) If you’re not sure what you’re getting into (or are scared a bit by the general description), I highly encourage to come and join us for at least the first few meetings before you pass up on the opportunity. I’m putting together a study group for an introduction to category theory. Who wants to join me?” – Chris Aldrich In some sense, we’re using this website as a means of communication between ourselves, but we’re also hoping to leave it behind to help other students (and autodidacts) in the future. So whether you’re in the initial peleton,” or you come across this in the future after we’ve all come and gone, feel free to sign up and add your own thoughts and comments to these pages. The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.” – David Spivak’s course description from his MIT class using his textbook Category Theory for the Sciences For a brief introduction to what we’re undertaking, please take a peek at the following pages, or browse through the menu: Syllabus Textbooks Resources Participants and the following initial posts: Category Theory Summer Study Group 2015 Category Theory Anyone? For those who need an introduction to the subject or some motivaton, you might find Ilyas Khan’s article Category Theory – the Bedrock of Mathematics? interesting. Though it tends a tad toward the technical side (so don’t let it scare you away – besides there’s a group of us here to help you!), it does show a little of the depth and breadth of what is going on in the subject. Want to join us? You can register as a participant to be allowed to add your own content here, or you can simply add your thoughts as comments to existing pages and posts. We look forward to welcoming you to the set of students who are studying category theory. Share this: Click to share on Twitter (Opens in new window) Click to share on Facebook (Opens in new window) Click to share on Google+ (Opens in new window) Click to share on LinkedIn (Opens in new window) Click to share on Reddit (Opens in new window) Click to share on Pocket (Opens in new window) Click to email this to a friend (Opens in new window) More Click to print (Opens in new window) Click to share on Tumblr (Opens in new window) Click to share on Pinterest (Opens in new window) Like this: Like Loading... Leave a Reply Cancel reply Summer Study Group 2015 Search for: Subscribe to Category Theory via Email Enter your email address to subscribe to this blog and receive notifications of new posts by email. Email Address Recent Posts Category Theory Lecture series from Steven Roman New meeting Week Ten Meeting: §5.1 and §5.2 of David Spivak’s Category Theory for the Sciences Remark about 5.1.1.13 Morphisms and homomorphisms Recent Comments HerbMartin on Videos HerbMartin on New meeting HerbMartin on Category Theory Lecture series from Steven Roman Chris Aldrich on Videos HerbMartin on Videos Categories Administrative Basic Category Theory (Chapter 5) Categories and Functors (Chapter 4) Category of Sets (Chapter 2) Category Theory Fundamental Considerations in Set (Chapter 3) Introdution (Chapter 1) Resources Tags abstract algebra abstract math administrative category theory commutative diagrams computer science CTAN David Spivak diagrams diagxy F. William Lawvere Florencio Neves graphs Ilyas Khan introduction Kristoffer Rose LaTeX manual mathematics Michael Barr Not Even Wrong Paul Taylor Peter Woit question resources review Ross Moore Saunders Mac Lane social media Stephen H. 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