Category Theory: Intro Texts & Recommended Books

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Discussion Overview

The discussion centers on recommendations for introductory texts on Category Theory, exploring various books and resources suitable for beginners in the field. Participants share their experiences with different texts and suggest alternatives based on varying levels of prior knowledge.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks recommendations for introductory books on Category Theory, expressing difficulty in finding suitable texts.
  • Another participant recommends "Basic Category Theory for Computer Scientists" by Benjamin C. Pierce as a straightforward option that requires minimal background knowledge.
  • A participant identifies "Categories for the Working Mathematician" by Saunders MacLane as the standard text for the subject.
  • Further recommendations include "Arrows, Structures and Functors: a categorical imperative" by Arbib for those less familiar with mathematical structures, and "Abstract and Concrete Categories" by Adamek, Herrlich, and Strecker, noted for its extensive examples and theoretical content, though considered more of a reference text.
  • One participant recalls that earlier standards included works by Peter Freyd and Barry Mitchell, questioning whether these texts cover general categories or are limited to abelian categories.
  • A suggestion is made regarding a video lecture series on YouTube, highlighting its clarity and the reputable source of the material, though it is noted that it should not replace a textbook.

Areas of Agreement / Disagreement

Participants express a variety of recommendations and experiences with different texts, indicating no consensus on a single standard introductory book. Multiple competing views on suitable resources remain present.

Contextual Notes

Some participants mention the varying levels of background knowledge required for different texts, indicating that certain recommendations may not be suitable for all beginners. The discussion also reflects a range of historical perspectives on standard texts in the field.

Who May Find This Useful

Individuals interested in starting their study of Category Theory, including students and professionals in mathematics and computer science, may find the recommendations and discussions valuable.

ForMyThunder
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I'm looking to start studying Category Theory. What books would you recommend for these? I can't seem to find an introductory book on categories. What is the standard text for such a thing?
 
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I read a book titled "Basic Category Theory for Computer Scientists" by Benjamin C.Pierce a few months ago. It is fairly short and straightforward and doesn't require a lot of background knowledge.
 
The standard book is Categories for the Working Mathematician by Saunders MacLane--one of the pioneers of the subject.
 
The usual reference is "Categories for the working mathematician" by MacLane. I suggest you read this, but I'll give some other references. Check them out and pick what you like best:

"Arrows, Structures and Functors: a categorical imperative" by Arbib is a good book if you're not very familiar to mathematical structures. MacLanes book already assumes that you're familier to a lot of things (like abstract algebra, topology,...). If you're not, then this book is better

"Abstract and concrete categories" by Adamek, Herrlich, Strecker is the very best book on categories! Furthermore, it is freely available on the website katmat.math.uni-bremen.de/acc/acc.pdf The book provides a lot of theory, and a massive amount of examples (the examples are really important for somebody studying categories!). However, I would consider the book more of a reference text than a textbook. But I really suggest reading this book together with MacLane!
 
Thanks so much for the material micromass! I've been very interested in Category theory recently as well. :D
 
when i was a kid the standards were those by peter freyd and by barry mitchell.
 
mathwonk said:
when i was a kid the standards were those by peter freyd and by barry mitchell.

Aren't these more for abelian categories? Or did they write stuff on general categories too, I may want to check those out!
 
I just think about it now, but they're is a great video lecture series on youtube: http://www.youtube.com/user/TheCatsters

I don't say that it's a substitute for a textbook, but the explanations are very clear! Definitely worth a look! Furthermore, the initiative comes from a university which is well-known for it's categories, so it's certainly good material...
 

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