🔖 [1803.05316] Seven Sketches in Compositionality: An Invitation to Applied Category Theory

Bookmarked Seven Sketches in Compositionality: An Invitation to Applied Category Theory by Brendan Fong, David I. Spivak (arxiv.org)
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. [.pdf]

This is the textbook that John Carlos Baez is going to use for his online course in Applied Category Theory.

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👓 Applied Category Theory – Online Course | John Carlos Baez

Read Applied Category Theory – Online Course by John Carlos BaezJohn Carlos Baez (Azimuth)
It just became a lot easier to learn about applied category theory, thanks to this free book:
• Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.

I’ve started an informal online course based on this book on the Azimuth Forum. I’m getting pretty sick of the superficial quality of my interactions on social media. This could be a way to do something more interesting.

The idea is that you can read chapters of this book, discuss them, try the exercises in the book, ask and answer questions, and maybe team up to create software that implements some of the ideas. I’ll try to keep things moving forward. For example, I’ll explain some stuff and try to help answer questions that people are stuck on. I may also give some talks or run discussions on Google Hangouts or similar software—but only when I have time: I’m more of a text-based guy. I may get really busy some times, and leave the rest of you alone for a while. But I like writing about math for at least 15 minutes a day, and more when I have time. Furthermore, I’m obsessed with applied category theory and plan to stay that way for at least a few more years.

If this sounds interesting, let me know here—and please visit the Azimuth Forum and register!

Some awesome news just as I’ve wrapped up a class on Algebraic Geometry and was actively looking to delve into some category theory over the summer. John Carlos Baez announced that he’s going to offer an online course in applied category theory. He’s also already posted some videos and details!

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Repost of John Carlos Baez’ Biology as Information Dynamics

Bookmarked Biology as Information Dynamics by John Carlos Baez (Google+)
I'm giving a talk at the Stanford Complexity Group this Thursday afternoon, April 20th. If you're around - like in Silicon Valley - please drop by! It will be in Clark S361 at 4 pm. Here's the idea. Everyone likes to say that biology is all about information. There's something true about this - just think about DNA. But what does this insight actually do for us? To figure it out, we need to do some work. Biology is also about things that can make copies of themselves. So it makes sense to figure out how information theory is connected to the 'replicator equation' — a simple model of population dynamics for self-replicating entities. To see the connection, we need to use relative information: the information of one probability distribution relative to another, also known as the Kullback–Leibler divergence. Then everything pops into sharp focus. It turns out that free energy — energy in forms that can actually be used, not just waste heat — is a special case of relative information Since the decrease of free energy is what drives chemical reactions, biochemistry is founded on relative information. But there's a lot more to it than this! Using relative information we can also see evolution as a learning process, fix the problems with Fisher's fundamental theorem of natural selection, and more. So this what I'll talk about! You can see slides of an old version here: http://math.ucr.edu/home/baez/bio_asu/ but my Stanford talk will be videotaped and it'll eventually be here: https://www.youtube.com/user/StanfordComplexity You can already see lots of cool talks at this location! #biology

Wondering if there’s a way I can manufacture a reason to head to Northern California this week…

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