
Applied Category Theory - mathgenius
https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/
======
danharaj
David Spivak has done lots of cool work on applying category theory to many
concrete systems like databases [1].

Brendan Fong has worked on applying category theory to things that act like
interconnected networks, such as electrical circuits. This fits into a larger
ambitious program that John Baez is part of to use category theory to
understand physical systems that are still much too complicated to understand
with current mathematical tools, such as ecosystems. Fong's thesis is on my
reading list [2].

The two authors are doing great research, like this investigation of the
algebra of backpropagation [3].

I really look forward to reading this too!

[1] [https://arxiv.org/abs/0904.2012](https://arxiv.org/abs/0904.2012)

[2] [https://arxiv.org/abs/1609.05382](https://arxiv.org/abs/1609.05382)

[3] [https://arxiv.org/abs/1711.10455](https://arxiv.org/abs/1711.10455)

~~~
tome
I made a Haskell Postgres library inspired by David Spivak's work:
[https://github.com/tomjaguarpaw/haskell-
opaleye/](https://github.com/tomjaguarpaw/haskell-opaleye/)

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jfaucett
This looks like a great resource. I really think the chapter difficulty idea
is a good one and wish more math books adopted this approach.

On another pedagogical note and as someone who reads a lot of math texts, I
wish math textbooks would spend way more time on introducing the intuition
(geometrical if in any way possible) of the ideas before or simultaneous with
going into the formulas, theorems, and details. This not only vastly improves
comprehension but I find having a geometrical understanding ( even if rough
and partially incorrect) greatly helps in me being able to later derive the
same formulas and theorems.

Having written about various math topics over the years I know its much more
difficult to follow this approach, so I don't blame anyone for not going out
of their way to imbue intuition, but its still something I wish more
mathematicians who teach would advocate for.

~~~
danield9tqh
Unfortunately from reading the first couple of chapters it seems like this
textbook doesn't do an excellent job of favoring graphics over formula. It's
acceptable but really nothing stellar. I don't think it does the title of
'Applied Category Theory' justice. It is still very much theoretical.

~~~
j2kun
Conveying intuition is about way more than using graphics. It's about
storytelling. I've seen people focus on graphics and fail in a hundred ways,
while overwhelming theoretical works shine due to the focus on the narrative.

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asavinov
Functional Programming and Category Theory:
[http://nikgrozev.com/2016/03/14/functional-programming-
and-c...](http://nikgrozev.com/2016/03/14/functional-programming-and-category-
theory-part-1-categories-and-functors/)

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unao
[http://math.mit.edu/~dspivak/teaching/sp18/](http://math.mit.edu/~dspivak/teaching/sp18/)

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empath75
As an interested amateur usually I find these ‘beginner’ texts laughably
impenetrable, but I had no problems following this all the way through chapter
one, at least.

It uses fairly simple language all the way through with lots of diagrams.

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signa11
for programmer's there is this :
[https://bartoszmilewski.com/2014/10/28/category-theory-
for-p...](https://bartoszmilewski.com/2014/10/28/category-theory-for-
programmers-the-preface/) as well.

~~~
alvarosevilla95
Having taken the course, I definitely recommend it. Great content and Bartosz
is just a great guy to listen to

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hollerith
I wish more PDFs written by academics had one column, not two, per page. The
2-column arrangement is harder for me to navigate when reading on a mobile
device. (The OP has one column.)

~~~
lou1306
I wish HTML/EPUB was as popular as PDF in academia... That would solve so many
problems for mobile reading.

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sadar_
As a mathematician, usually I find attempts to apply abstract mathematical
concepts to concrete real-world concepts clumsy and hurting both the
abstraction and the concrete thing.

Is this the case with this text?

~~~
nine_k
If one cannot apply mathematics to concrete things, what use does the
mathematics have, besides mental gymnastics?

If mathematics is applied poorly to reality, it's usually because an
inadequate model is used, not because attempting this is a wrong thing to do.

~~~
sadar_
First of all, when I said concrete things I did not mean for example
theoretical physics concepts. I mean things like economics[0] or
philosophy[1].

I am saying that mathematical abstraction is not the right tool to get a
better understanding for a lot of subjects. My questions was asking if this is
an instance of someone with a categorical hammer and seeing categorical nails
everywhere, or that it is a super natural fit.

Most mathematicians (I know) do mathematics for the mathematics. It is in
itself a goal that does not need an external use. So yes, mathematics for a
lot of mathematicians is just mental gymnastics that turned out to be very
useful. Probably the reasons for some people's love for math and the
usefulness are related.

[0] [https://www.quora.com/Are-there-applications-of-group-
theory...](https://www.quora.com/Are-there-applications-of-group-theory-in-
economics)

[1]
[https://en.wikipedia.org/wiki/Alain_Badiou#Mathematics_as_on...](https://en.wikipedia.org/wiki/Alain_Badiou#Mathematics_as_ontology)

~~~
pensativo
Category theory is a formal semantics for (or alternative to, depending on
one's perspective) type theory and thus functional programming. It's been
widely used (for example, in Haskell, ML, Agda, Coq, Idris, etc) not only for
formal foundations but to derive many "smaller" practical applications. Many
of the creations from that domain have been useful in many other languages.
Are you unaware of this and asking something else?

It's an extremely good fit and highly productive, to answer your question
directly.

~~~
sadar_
I am aware of these applications. I am not aware of any "smaller" practical
applications that are derived thanks to the categorical interpretation, can
you give any examples?

~~~
danharaj
[https://arxiv.org/abs/1502.05947](https://arxiv.org/abs/1502.05947)

 _In this paper we describe a functorial data migration scenario about the
manufacturing service capability of a distributed supply chain. The scenario
is a category-theoretic analog of an OWL ontology-based semantic enrichment
scenario developed at the National Institute of Standards and Technology
(NIST). The scenario is presented using, and is included with, the open-source
FQL tool, available for download at categoricaldata.net /fql.html._

This is part of a series of work on applying category theory to databases. The
initial work was to cast database concepts into categorical concepts, this led
to a clarification of various concepts such as many kinds of SQL query being
instances of limits and colimits. The theory was then used to extrapolate via
category theoretic concepts to develop new database manipulation concepts.

This is a general recipe for applying category theory, though there are other
approaches.

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codekilla
This is really great! For those interested, another book on the way is:
[http://www.sci.brooklyn.cuny.edu/~noson/MCtext.html](http://www.sci.brooklyn.cuny.edu/~noson/MCtext.html).
I've read Noson's other book on Quantum Computing and it was really clear,
with lot's of examples.

~~~
jesuslop
Yeah the other book is very sweet and accesible, and quantum computing is very
amenable to the monoidal category treatment as Coecke shows pleasantly in
'Picturing Quantum Processes', 110710422X.

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dragon96
The associated video lectures can be found on the course homepage here:
[http://math.mit.edu/~dspivak/teaching/sp18/](http://math.mit.edu/~dspivak/teaching/sp18/)

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bitforger
I'd like to buy a hard copy of this... is it in print anywhere? Alternatively
I'll just print the whole thing out I suppose.

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jpfed
So the text looks promising but, just as importantly, can someone just make a
whole cookbook with diagrams like that?

~~~
defen
[http://www.cookingforengineers.com/](http://www.cookingforengineers.com/) has
a a slightly more primitive version in their recipes. Example:
[http://www.cookingforengineers.com/recipe/58/Peanut-
Butter-C...](http://www.cookingforengineers.com/recipe/58/Peanut-Butter-
Cookies) (scroll down to just before the comments)

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kummapp
I would prefer this kind of notion with the categories:

[https://github.com/kummahiih/python-domain-
equations](https://github.com/kummahiih/python-domain-equations)

but seems like, I am the only one who likes simplicity

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zombieprocesses
Wikibooks has a very basic intro to category theory/haskell.

[https://en.wikibooks.org/wiki/Haskell/Category_theory](https://en.wikibooks.org/wiki/Haskell/Category_theory)

