Seven Sketches in Compositionality: An Invitation to Applied Category Theory · HackerPapers discussions

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by cirpis

Sat, 07 Sep 2024 14:05:02 GMT

This seems like a needlesly defensive answer. If there are no examples then just say so. It is mathematics after all, some of it is beautiful to explore just for its own sake, no examples or applications neccesary. But claiming a technique is a bridge between disparate areas of mathematics and then subsequently failing to give concrete examples of such bridging is a bit odd, dont you think? For what its worth the book "7 sketches in compositionality" (https://arxiv.org/abs/1803.05316) has a chapter on topos theory which provides a good introduction with some simple examples!

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by lgas

Fri, 10 Mar 2023 02:53:59 GMT

How about https://arxiv.org/abs/1803.05316?

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by Twisol

Sun, 25 Dec 2022 05:35:25 GMT

As I understand it, submissions are moderated (albeit lightly -- not to the degree of formal peer review). So, since it's on the arXiv, we can assume that the moderators felt it belongs there. I've seen a number of other book-length items on the arXiv before, including e.g. Seven Sketches in Compositionality [1], so this isn't a particularly new trend, either. [1] https://arxiv.org/abs/1803.05316v3

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by lgdw

Tue, 01 Nov 2022 17:03:46 GMT

If anyone is interested in Applied Category Theory, definitely check out the Topos Institute in Berkeley [1]. They do weekly seminars that they post on youtube and a really intriguing blog. I must say that David Spivak is a treasure to hear speak. 7 Sketches in Compositionality [2] was my introduction into Category Theory (written by Spivak and Brendan Fong, another member of Topos), and it really sold the idea of Category Theory as a field that's not just a mathematical meta-language but also a field that can stand on its own. I recommend it over Mac Lane's CWM if you're not a mathematician.…

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Sat, 14 May 2022 21:34:45 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by co_dh

Sat, 14 May 2022 20:26:43 GMT

https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Fri, 22 Oct 2021 17:59:40 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by jkhdigital

Fri, 22 Oct 2021 11:09:16 GMT

I’m currently taking a category theory course based on Fong & Spivak’s textbook An Invitation to Applied Category Theory [1] and this reminds me of chapter 3 which introduces functors and natural transformations by way of using them to describe schemas, database instances and migrations. [1] https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by hkopp

Thu, 16 Sep 2021 06:52:14 GMT

I would recommend "Seven Sketches in Compositionality", as it does not progressively get harder, but each chapter starts off very easily. So you can catch up, if you got lost. It is available here: https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by zozbot234

Thu, 29 Apr 2021 18:42:18 GMT

Newer work from the same author: Seven Sketches in Compositionality: An Invitation to Applied Category Theory https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by benrbray

Thu, 01 Apr 2021 11:40:57 GMT

If you’re curious about this stuff and don’t know where to begin, the first chapter of Fong & Spivak, “An Invitation to Applied Category Theory: Seven Sketches in Compositionality” [1] also introduces category-theoretic ideas using partial orders. Edit: After the Fong & Spivak book, the book by Emily Riehl, "Category Theory in Context" is an excellent next step, although it requires some mathematical maturity. [1]: https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by mathcass

Wed, 03 Feb 2021 03:15:32 GMT

I have a disclaimer. I'm not an expert in category theory at all. However, my primary background is in mathematics and I've "looked over the basics" as they say. If you'll allow me to dodge the question just a little bit, I'd recommend that you dive in and see what it feels like to start learning it. The way I think that could proceed is to a) go find a book, lecture, video, or other resource you'd like to engage with, and b) start devouring it. If you run into conceptual difficulties, start looking online for ways to explain that difficult concept to yourself so that you can proceed.…

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by Fishysoup

Mon, 31 Aug 2020 20:33:30 GMT

This has probably been posted before but since Category Theory has been popping up every once in a while I thought I'd share this. I'm just starting this and the instructors' [book](https://arxiv.org/abs/1803.05316) here, and the subject is very approachable even for biologists like myself.

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by shaunxcode

Sat, 04 Jul 2020 00:13:07 GMT

link to read online: https://arxiv.org/pdf/1803.05316.pdf

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by Kinrany

Sun, 03 May 2020 11:02:02 GMT

I initially decided against posting the video because the thread has a small amount of discussion. Mainly the link to related work: Seven Sketches in Compositionality, https://arxiv.org/abs/1803.05316 Edit: previously on HN: https://news.ycombinator.com/item?id=20376325

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by gsjbjt

Tue, 07 Apr 2020 02:29:40 GMT

David Spivak and Brendan Fong have been doing lots of work at MIT to evangelize applied category theory. See their recent books/classes: Seven Sketches in Compositionality: An Invitation to Applied Category Theory https://arxiv.org/abs/1803.05316 Applied Category Theory mini-course: https://ocw.mit.edu/courses/mathematics/18-s097-applied-cate... Programming with Categories mini-course (with Bartosz Milewski): http://brendanfong.com/programmingcats.html

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by nextos

Tue, 14 Jan 2020 21:53:01 GMT

As a Lisper, I love Clojure and all Rich Hickey does. However, Haskell and categories seem to offer quite appealing approaches to compositionality: http://conal.net/talks/compiling-to-categories.pdf https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by zozbot234

Wed, 01 Jan 2020 02:18:19 GMT

What kinds of graphs? There are a number of graphical representations that turn out to be incredibly useful in category theory, but they're far from equivalent. IIRC, https://arxiv.org/abs/1803.05316 introduces some of them.

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by agentultra

Mon, 16 Dec 2019 14:48:44 GMT

Going to finish Crime and Punishment, Year of the Monkey (Patti Smith), The Children of Húrin (along with many cross references and letters) (Tolkien), re-reading A Game of Thrones for fun... as for 2020 I might read Slaughterhouse 5 again and work through George Sand. Technical things I am working through are the: - https://www.extension.harvard.edu/open-learning-initiative/a... along with the Artin text, writing proofs out by hand and in Lean. - Seven Sketches in Compositionality: https://arxiv.org/abs/1803.05316

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by ltr_

Tue, 27 Aug 2019 11:29:35 GMT

aside from 3Blue1Brown : I think category theory will give you an unique point of view of math, also basic logic and philosophy are very important for a good and solid foundation on math intuition. https://arxiv.org/abs/1803.05316 along with their youtube lectures. very basic but refreshing: https://www.youtube.com/playlist?list=PL8dPuuaLjXtNgK6MZucdY... if you are a programmer or developer: https://bartoszmilewski.com/2014/10/28/category-theory-for-p... https://blog.ploeh.dk/2017/10/04/from-design-patterns-to-cat...

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Sun, 07 Jul 2019 17:31:58 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

294 points; 36 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Fri, 17 May 2019 21:05:39 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by chombier

Sat, 20 Apr 2019 07:18:46 GMT

I am currently reading it, it is very nicely written and accessible. Each chapter starts off gently so you can skip to the next whenever you feel lost, only to come back later. So far: introduction/preorders, monoidal preorders/wiring diagrams, categories/application to database schemas. For those reading on a ebook, the book sources are available on its arxiv page https://arxiv.org/abs/1803.05316 so you can build a custom pdf for your device.

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by 0815test

Sat, 16 Mar 2019 14:59:00 GMT

The mnemonic value of "operators" as reminders of properties such as associativity or commutativity interestingly extends to diagrammatic reasoning. A diagram is really just a generalized expression, and this becomes quite useful when one has to deal with more than one "type" or "domain" of operation, but in a consistent way that preserves the compositionality-like properties OP talks about. A recent book exploring this topic is "Seven Sketches in Compositionality; An Invitation to Applied Category Theory" https://arxiv.org/abs/1803.05316 . (Despite the obvious reference to CT in the title…

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — mentioned by zozbot123

Sun, 10 Feb 2019 21:58:17 GMT

Somewhat less of a "textbook", but good at showing applications of category theory - Fong, Spivak: Seven Sketches in Compositionality https://arxiv.org/abs/1803.05316 (Notably, this includes application to a "graphical" treatment of fairly-elementary linear algebra, which a different HN user is mentioning even as I write this, as a part of math where CT cannot possibly be useful and will only ever confuse students!)

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Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Sun, 13 May 2018 19:07:30 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Mon, 26 Mar 2018 19:15:55 GMT

An Invitation to Applied Category Theory

1 point; 1 discussion reply on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Mon, 26 Mar 2018 08:02:49 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Seven Sketches in Compositionality: An Invitation to Applied Category Theory — HN submission

Thu, 15 Mar 2018 16:50:43 GMT

Seven Sketches in Compositionality: An Invitation to Applied Category Theory

4 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.