Where Can I Find a Quick Start Guide for Learning Category Theory?

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Discussion Overview

The discussion centers on finding resources for learning category theory, particularly for someone with a background in undergraduate abstract algebra. Participants share recommendations for books and approaches to studying the subject, considering the varying levels of prior knowledge and motivation for learning.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant suggests starting with MacLane's "Categories for the Working Mathematician," noting it assumes familiarity with algebra and algebraic topology.
  • Another participant recommends Goldblatt's "Topoi: The Categorical Analysis of Logic," which covers basic category theory and topoi theory, and is available for free online, but mentions it lacks many practical examples.
  • A participant questions the motivation for learning category theory, suggesting that without a solid background, it may be challenging to grasp the material, as category theory is often applied in fields like algebraic geometry and algebraic topology.
  • One participant expresses a desire to understand category theory concepts as they relate to algebraic geometry, rather than pursuing deep knowledge.
  • Another participant mentions learning category theory from Hungerford's Algebra, indicating that specific chapters may suffice for the original poster's needs.
  • A later reply suggests that actively proving concepts and working through examples could enhance understanding of category theory, referencing personal experience with Yoneda's lemma as a learning tool.

Areas of Agreement / Disagreement

Participants express varying opinions on the necessity of prior knowledge and the best resources for learning category theory. There is no consensus on a single approach or resource, and motivations for learning differ among participants.

Contextual Notes

Some participants note the importance of background knowledge in algebra and related fields for understanding category theory, while others emphasize the need for practical examples and applications to motivate learning.

matness
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I am only familiar to undergrad abstract algebra and want to learn category theory.
which book or website do you suggest for a quick start?
thanks in advance
 
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So before I give any suggestions, you should know that I probably have less of a background in algebra than you and also haven't yet learned much Category Theory (but I work on it sometimes in my free time).

A while ago, I started a topic where I asked a similar question and did some reading through some books before picking one to start learning from.

The standard text on Category Theory is MacLane's Categories for the Working Mathematician, but it assumes that you're already familiar with a lot of algebra. In particular, I believe that it assumes some knowledge of algebraic topology.

Goldblatt has a book titled Topoi: The Categorical Analysis of Logic. It builds up all of the basic category theory and eventually covers a good deal. It also covers some basic topoi theory. It assumes that you have a fair grasp of undergrad algebra (but it is not necessary that you do).
Additionally, you can read the book for free here: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=Gold010&seq=&view=75&frames=0&pagenum=
(Although I don't have a link to Goldblatt's website at this moment, the above link is on his website)
The only problem that I've noticed with the book is that it doesn't seem to have many examples of applications of the earlier ideas. It mainly builds up the basics so that it can get to Topos Theory
That is the book that I am working through at the moment.
 
Why do you want to learn category theory? If you just want to learn it for the sake of learning it, I think it will be tough to digest it without having more background than you mentioned. Despite what some people may think, category theory's purpose is for applications to other math (like algebraic geometry and algebraic topology) and not abstraction for its own sake.

It might be better to start with some homological algebra or algebraic topology so that the stuff you see will be motivated.
 
masnevets said:
Why do you want to learn category theory?.

Because in algebraic geometry lots of things are explained in terms of categories and functors.Not want deeply learning this stuff but understanding when it is used in definitions thm s etc.
 
All the category theory I know (which is not a lot), I learned from chapters I and X of Hungerford's Algebra. It sounds like these two chapters (well, section and a chapter!) will be good enough for you too.
 
matness said:
Because in algebraic geometry lots of things are explained in terms of categories and functors.Not want deeply learning this stuff but understanding when it is used in definitions thm s etc.

In that case, I think the best way to learn category theory is to try and prove some of the things yourself and work out a bunch of examples. I never really understood what a natural transformation was until I was assigned Yoneda's lemma on a problem set. This might not be a bad way to go. In the process I think you would pick up a lot of valuable definitions.
 

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