Best book/tutorial on category theory and its applications
Hi, I would like to buy some booke on category theory and its applications. Can you recommend me the best? Here is what I like: 1. Easy to understatnd, concise book. I like e.g. "Gentle introduction to Haskell" it was quite good with a little of text. There are bigger tutorials in number of pages but there is much less in them. I downloaded "Categories for Software Engineering". I read 2 first chapters, but there is a lot of text and sometimes I need to look on internet to seach for exact definitions/equations which I can understand better. That's why I don't like books "for Dummies" - lot of text, little of content, very shallow and lot of slang. I like "The Haskell: School of expression" and I am searching for another book to read after I finish this. The style of SOE is suitable for me. It is very clear with good theory and examples. But now I want book mainly about theory and the examples as second. 2. With applications and its examples. I would like to see some examples. I doesn't matter if it will be only in pseudo-language in Haskell or another language. What do you think about "Categories and Computer Science (Cambridge Computer Science Texts)" at http://www.amazon.com/Categories-Computer-Science-Cambridge-Texts/dp/0521422... ? Thanks Fero -- View this message in context: http://www.nabble.com/Best-book-tutorial-on-category-theory-and-its-applicat... Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.
On Mon, 28 Jul 2008 01:41:50 -0700 (PDT), fero
Hi, I would like to buy some booke on category theory and its applications. Can you recommend me the best?
Recently, I had to study some category theory in order to prepare for a local category theory study group meeting, and after some comparison, settled on the following relatively short set (128 pp.) of notes, condensed from a much thicker book (303 pp.) on category theory: Category Theory Lecture Notes for ESSLLI Michael Barr, Department of Mathematics and Statistics, McGill University Charles Wells, Department of Mathematics, Case Western Reserve University http://www.math.upatras.gr/~cdrossos/Docs/B-W-LectureNotes.pdf The above-mentioned lecture notes were condensed from the following book, and then rearranged to present category theory from a computer science perspective: Toposes, Triples and Theories by Michael Barr and Charles Wells http://www.cwru.edu/artsci/math/wells/pub/ttt.html According to the above-referenced home page for this book:
The original book, Grundlehren der math. Wissenschaften 278. Springer-Verlag, 1983, is now out of print. A revised and corrected version is now available free for downloading.
An even shorter book on category theory is the following: A Gentle Introduction to Category Theory - the calculational approach by Maarten M Fokkinga http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html However, I did not prefer the above book, despite its brevity, because unlike the other two titles, it did not including any specific material on monads.
What do you think about "Categories and Computer Science (Cambridge Computer Science Texts)" at http://www.amazon.com/Categories-Computer-Science-Cambridge-Texts/dp/0521422... ?
I haven't read it, so I would need to review it before giving an opinion. I shall keep it in mind, however; thank you for the reference. -- Benjamin L. Russell
On Mon, 28 Jul 2008 20:04:17 +0900, Benjamin L.Russell
What do you think about "Categories and Computer Science (Cambridge Computer Science Texts)" at http://www.amazon.com/Categories-Computer-Science-Cambridge-Texts/dp/0521422... ?
I haven't read it, so I would need to review it before giving an opinion. I shall keep it in mind, however; thank you for the reference.
I have just added information on _Categories and Computer Science (Cambridge Computer Science Texts)_ to the HaskellWiki; viz.: Books and tutorials - HaskellWiki http://www.haskell.org/haskellwiki/Books_and_tutorials Incidentally, my earlier references to books on category theory all originally were obtained from the HaskellWiki page on Category Theory: Category theory - HaskellWiki http://haskell.org/haskellwiki/Category_theory#See_also You may find some other useful references there as well. -- Benjamin L. Russell
Thanks Benjamin,
especially for http://haskell.org/haskellwiki/Category_theory#See_also and I
found there Haskell wiki. I will take a look at the books as well.
Fero
On Mon, Jul 28, 2008 at 2:14 PM, Benjamin L. Russell wrote: On Mon, 28 Jul 2008 20:04:17 +0900, Benjamin L.Russell
What do you think about "Categories and Computer Science (Cambridge
Computer
Science Texts)" at http://www.amazon.com/Categories-Computer-Science-Cambridge-Texts/dp/0521422... ? I haven't read it, so I would need to review it before giving an
opinion. I shall keep it in mind, however; thank you for the
reference. I have just added information on _Categories and Computer Science
(Cambridge Computer Science Texts)_ to the HaskellWiki; viz.: Books and tutorials - HaskellWiki
http://www.haskell.org/haskellwiki/Books_and_tutorials Incidentally, my earlier references to books on category theory all
originally were obtained from the HaskellWiki page on Category Theory: Category theory - HaskellWiki
http://haskell.org/haskellwiki/Category_theory#See_also You may find some other useful references there as well. -- Benjamin L. Russell _______________________________________________
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Haskell-Cafe@haskell.org
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On Mon, Jul 28, 2008 at 5:04 AM, Benjamin L. Russell
Category Theory Lecture Notes for ESSLLI Michael Barr, Department of Mathematics and Statistics, McGill University Charles Wells, Department of Mathematics, Case Western Reserve University http://www.math.upatras.gr/~cdrossos/Docs/B-W-LectureNotes.pdf
So far this has been an excellent read for someone failing to grok category theory for a while! Thanks! Luke
The above-mentioned lecture notes were condensed from the following book, and then rearranged to present category theory from a computer science perspective:
Toposes, Triples and Theories by Michael Barr and Charles Wells http://www.cwru.edu/artsci/math/wells/pub/ttt.html
According to the above-referenced home page for this book:
The original book, Grundlehren der math. Wissenschaften 278. Springer-Verlag, 1983, is now out of print. A revised and corrected version is now available free for downloading.
An even shorter book on category theory is the following:
A Gentle Introduction to Category Theory - the calculational approach by Maarten M Fokkinga http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html
However, I did not prefer the above book, despite its brevity, because unlike the other two titles, it did not including any specific material on monads.
What do you think about "Categories and Computer Science (Cambridge Computer Science Texts)" at http://www.amazon.com/Categories-Computer-Science-Cambridge-Texts/dp/0521422... ?
I haven't read it, so I would need to review it before giving an opinion. I shall keep it in mind, however; thank you for the reference.
-- Benjamin L. Russell
_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
I've only read the beginning, but I recommend _Conceptual Mathematics_ by Lawvere and Schanuel for a *very* gentle introduction (seriously, you could probably teach category theory to ten-year-olds out of this book.) Nothing about applications there, though. Cheers, Tim -- Tim Chevalier * http://cs.pdx.edu/~tjc * Often in error, never in doubt "I haven't got the slightest idea how to change people, but still I keep a long list of prospective candidates just in case I should ever figure it out." --David Sedaris
On Mon, 28 Jul 2008 11:52:43 -0700, "Tim Chevalier"
I've only read the beginning, but I recommend _Conceptual Mathematics_ by Lawvere and Schanuel for a *very* gentle introduction (seriously, you could probably teach category theory to ten-year-olds out of this book.) Nothing about applications there, though.
Does _Conceptual Mathematics_ discuss monads? -- Benjamin L. Russell
Does _Conceptual Mathematics_ discuss monads?
I'm currently working on it, I'm at section 13 with Monoids but there are no Monads at the horizon. I have briefly gone through the end of the book and did not recognize anything similar to a Monad. But I might not be able to recognize a Monad in a category theory presentation, though. However, as a complete n00b in category theory, I find this book perfect. I tried Mac Lane's book ("Categories for the working mathematician") first but I was distracted by the notations and the long, painful mathematical sentences. Nevertheless, none of these books are computer scientist-oriented. I have been recommended "Categories for Types" by Crole. I plan to work on it after Conceptual Mathematic and Mac Lane's book. Right now, I've now real opinion about it: at first glance, it looks as technical as Mac Lane's book. I believe some enlightened people here could give more useful review of it. HTH, -- Pierre-Evariste DAGAND http://perso.eleves.bretagne.ens-cachan.fr/~dagand/
If you want to see a human being explain some categorical ideas, there is a nice (and growing) collection of video mini-tutorials on youtube by the Catsters. http://www.youtube.com/user/TheCatsters -Nathan Bloomfield (I first sent this just to Pierre by accident - sorry!)
fero asked:
Hi, I would like to buy some booke on category theory and its applications. Can you recommend me the best?
I got a lot out of Basic Category Theory for Computer Scientists by Benjamin C. Pierce. Short and with examples biased towards CS. No monads but it covers the essentials with F-algebras as a bonus. Finishes with some extended CS-motivated examples. -- Dan
fero
What do you think about "Categories and Computer Science (Cambridge Computer Science Texts)" at http://www.amazon.com/Categories-Computer-Science-Cambridge-
Texts/dp/0521422264/ref=si3_rdr_bb_product
?
I couldn't see monads or the Yoneda lemma in the index. As a Haskell programmer, the lack of the former might be a concern; the latter is a standard result. Dominic.
participants (9)
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Benjamin L.Russell -
Dan Piponi -
Dominic Steinitz -
fero -
frantisek kocun
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Luke Palmer -
Nathan Bloomfield -
Pierre-Evariste Dagand -
Tim Chevalier