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September 18, 2018

What is Applied Category Theory?

Posted by John Baez

Tai-Danae Bradley has a new free book:

Abstract. This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and compositionality), two constructions (monoidal categories and decorated cospans) and two examples (chemical reaction networks and natural language processing) within the field.

This book grew out of the workshop Applied Category Theory 2018, which she attended. I think it makes a great complement to Fong and Spivak’s Seven Sketches and my online course.

Check it out!

Posted at September 18, 2018 7:44 PM UTC

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6 Comments & 0 Trackbacks

Re: What is Applied Category Theory?

This is really good! I especially like the explanation of functorial semantics.

We definitely need more of this, people out there need to know what we are doing :)

Posted by: Paolo Perrone on September 19, 2018 11:24 AM | Permalink | Reply to this

Re: What is Applied Category Theory?

As Tai-Danae Bradley writes, category theory has always been applied.

Have you seen Eilenberg’s giant treatise on automata theory from 1974/1976 ?

But hey, keep up the good marketing !

Posted by: David Espinosa on September 26, 2018 10:13 AM | Permalink | Reply to this

Re: What is Applied Category Theory?

To clarify, I don’t accept that you have invented applied category theory.

If you had said, “We’re working in applied category theory, but we didn’t invent it”, I wouldn’t mind.

Or if you had said, “We’re working in categorical network theory, and we’ve made some essential new contributions”, I wouldn’t mind.

But the combination of the overly broad description and the claim of invention is hard to take.

Posted by: David Espinosa on September 26, 2018 10:27 AM | Permalink | Reply to this

Re: What is Applied Category Theory?

Here’s another example – Joseph Goguen had an entire career in applied category theory, before you guys even got started:

https://en.wikipedia.org/wiki/Joseph_Goguen

Posted by: David Espinosa on September 26, 2018 10:40 AM | Permalink | Reply to this

Re: What is Applied Category Theory?

Hello. There’s an ongoing discussion here about it. You are welcome to join it there (constructively), many people are pointing out similar problems as you are.

(About the name “applied category theory”, I agree it may be not the most accurate, but what would be a good alternative? See the discussion there.)

Posted by: Paolo Perrone on September 26, 2018 11:17 AM | Permalink | Reply to this

Re: What is Applied Category Theory?

David wrote:

To clarify, I don’t accept that you have invented applied category theory.

Huh? Who do you think claimed to have invented it? Me? Tai-Danae Bradley? I don’t get it.

Oh, maybe I can guess what’s going on here. When I wrote:

Tai-Danae Bradley has a new free “booklet” on applied category theory. It grew out of the workshop Applied Category Theory 2018.

I meant that her book grew out of this workshop, not that applied category theory grew out of this workshop. Her book is largely about two examples that were discussed in this workshop.

I will edit this. I never imagined that “it” would be read this way.

Posted by: John Baez on September 26, 2018 7:56 PM | Permalink | Reply to this

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