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Basic Category Theory for Computer Scientists

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Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightf Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts.


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Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightf Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts.

30 review for Basic Category Theory for Computer Scientists

  1. 5 out of 5

    Sandy Maguire

    Terse. Maybe too terse, but a lot of my issues would have been resolved had I realized there was an appendix of notation at the back of the book. Serves as a pretty solid introduction to category theory, but provides absolutely no indication as to *why one might want to know category theory*. The treatment is primarily for organizing ones thoughts about abstract structures rather than actually working with them. The book very briefly mentions representability, with no discussion of the Yoneda le Terse. Maybe too terse, but a lot of my issues would have been resolved had I realized there was an appendix of notation at the back of the book. Serves as a pretty solid introduction to category theory, but provides absolutely no indication as to *why one might want to know category theory*. The treatment is primarily for organizing ones thoughts about abstract structures rather than actually working with them. The book very briefly mentions representability, with no discussion of the Yoneda lemma (which I understand to be one of the more useful parts of category theory). I read this as part of MIRI's recommended reading list.

  2. 4 out of 5

    Forest Tong

    I really enjoyed the first two chapters, which provide an extremely brief and accessible introduction to basic concepts of category theory (products, equalizers, functors, adjoints, etc.) with good exercises. However, the third chapter, which discusses applications to computer science, predominantly consisted of a lengthy theoretical discussion of recursive domain equations requiring background in domain theory, which I lack. I also wish the author had talked more about the connection between ca I really enjoyed the first two chapters, which provide an extremely brief and accessible introduction to basic concepts of category theory (products, equalizers, functors, adjoints, etc.) with good exercises. However, the third chapter, which discusses applications to computer science, predominantly consisted of a lengthy theoretical discussion of recursive domain equations requiring background in domain theory, which I lack. I also wish the author had talked more about the connection between category theory and logic.

  3. 5 out of 5

    Saeede Kermani

    کتگوری بخونید ولی از روی کتاب استیو آودی، اگه ریاضی بلد نیستین هم به نظرم هیچ وقت نمیفهمین اینایی که میخونین به چه درد میخوره پس نخونین... من با استاد و کتاب آودی و تجربهی دست پا شکستهی ریاضی به سختی متوجه شدم کتگوری چیه... کتگوری بخونید ولی از روی کتاب استیو آودی، اگه ریاضی بلد نیستین هم به نظرم هیچ وقت نمی‌فهمین اینایی که می‌خونین به چه درد می‌خوره پس نخونین... من با استاد و کتاب آودی و تجربه‌ی دست پا شکسته‌ی ریاضی به سختی متوجه شدم کتگوری چیه...

  4. 5 out of 5

    Tikhon Jelvis

    A surprisingly accessible introduction to category theory. It really helped me get a grasp on the different ideas I had seen earlier and filled in some of the parts I hadn't. The book was a bit too succinct at points--the only reason I got through most of it quickly was because I was already familiar with the material. The genuinely novel parts of the book took quite a bit more effort to get through. Nonetheless, it was still much more accessible than other books on the same subject! A surprisingly accessible introduction to category theory. It really helped me get a grasp on the different ideas I had seen earlier and filled in some of the parts I hadn't. The book was a bit too succinct at points--the only reason I got through most of it quickly was because I was already familiar with the material. The genuinely novel parts of the book took quite a bit more effort to get through. Nonetheless, it was still much more accessible than other books on the same subject! This is very much only a cursory introduction. It's certainly enough for the discerning functional programmer, but not enough to follow many current PL theory papers. Also not enough to use some of ekmett's libraries like category-extras :).

  5. 5 out of 5

    Tim

    Good book, nicely introduces just enough category theory to understand slightly more advanced texts. Perfect for graduate CS or undergraduate Maths students but perhaps a bit too brief for undergrad CS, assumes decent knowledge of set theory and algebra, for example knowledge of monoids is assumed and not really covered. Covers functors and natural transformations nicely though. Has a truly excellent bibliography and further reading chapter, pointing out many introductory books, reference books, Good book, nicely introduces just enough category theory to understand slightly more advanced texts. Perfect for graduate CS or undergraduate Maths students but perhaps a bit too brief for undergrad CS, assumes decent knowledge of set theory and algebra, for example knowledge of monoids is assumed and not really covered. Covers functors and natural transformations nicely though. Has a truly excellent bibliography and further reading chapter, pointing out many introductory books, reference books, articles and research papers.

  6. 5 out of 5

    Leonardo

    It's a pity this book is so short. Although some concepts flew straight over my head, I got quite a bit out of it. It's really interesting to see the application of Category Theory to programming language design, in particular to the foundational theory behind things like function application, currying, implicit conversions and generic operations. If you read this and you're left wanting more, the bibliography at the end of the book is a great resource to deepen your knowledge.

  7. 5 out of 5

    Paul Graphov

    I'am not a computer scientist actually, just a software developer. The book is a bit too succinct, making some things harder to catch. On the other hand it gives good picture in quite a few pages. Also it was quite exciting to see parallels between different concepts when viewing from categorical point. Also huge "Further reading" part gives directions for ones who want to go deeper.

  8. 4 out of 5

    Ushan

    This book presents some basic notions from category theory and tries to apply them to computer science - for example, generic data types are like functors: List carries T into lists of T and functions on T into functions on lists of T via mapcar. I don't find it terribly useful. It may or may not be nonsense, but it is exceedingly abstract.

  9. 5 out of 5

    Nick

    Certainly there's more I could have gotten out of this book. I could have dug deeper, worked through exercises and examples carefully, etc. And I only really skimmed the final chapter on applications to CS, which seems like what I should have taken as the highlight. I did, though, enjoy some of the examples in the second chapter, such as seeing how floor and ceiling were adjoints.

  10. 4 out of 5

    Jakub

    While this book is an interesting read, it is definitely NOT BASIC. I've had a hard time understanding many of the concepts in the way they're explained, even though this isn't the first thing I've read about Category Theory. There are many prerequisites to be able to understand the content, set theory being one, but not the only one.

  11. 5 out of 5

    Nick Black

    Everything I've read by Benjamin Pierce has been awesome, and I'm going to need to get into category theory more heavily pretty soon now (definitely by next Fall semester)...anyone have some recommendations (Brian McNamara, this means you)?

  12. 4 out of 5

    George Leontiev

    Great introduction to the main concepts, good list of the followup literature.

  13. 4 out of 5

    Debasish Ghosh

    Solid authoritative text. But definitely needs a prerequisite of linear algebra.

  14. 5 out of 5

    Daniel

    Far too little to effectively teach a subject as abstract as category theory. But the bibliography alone might be worth $20...

  15. 5 out of 5

    Michael

    A few more reads should bring gradual understanding.

  16. 5 out of 5

    Mark Moon

    This is the most concise introductory category theory book I've seen so far.

  17. 4 out of 5

    Peng Wang

  18. 5 out of 5

    Oliver Steele

  19. 5 out of 5

    Irene

  20. 5 out of 5

    Rob Norris

  21. 4 out of 5

    Andy Legkiy

  22. 4 out of 5

    Alejandro

  23. 4 out of 5

    Erik

  24. 5 out of 5

    Vik

  25. 4 out of 5

    Jason Silva

  26. 4 out of 5

    Jiaming Jiang

  27. 4 out of 5

    R* Grannell

  28. 5 out of 5

    Bar Shirtcliff

  29. 4 out of 5

    Geoff

  30. 5 out of 5

    Yosuke

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