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Basic Category Theory

Basic Category Theory

Basic Category Theory

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Year:2016
Publisher:University of Edinburgh
Pages:191 pages
Language:english
Since:16/02/2017
Size:1.29 MB
License:CC-BY-NC-SA

Content:

This is not a sophisticated text. In writing it, I have assumed no more mathematical knowledge than might be acquired from an undergraduate degree at an ordinary British university, and I have not assumed that you are used to learning mathematics by reading a book rather than attending lectures. Furthermore, the list of topics covered is deliberately short, omitting all but the most fundamental parts of category theory. A ‘further reading’ section points to suitable follow-on texts.

There are two things that every reader should know about this book. One concerns the examples, and the other is about the exercises. Each new concept is illustrated with a generous supply of examples, but it is not necessary to understand them all. In courses I have taught based on earlier versions of this text, probably no student has had the background to understand every example. All that matters is to understand enough examples that you can connect the new concepts with mathematics that you already know.

As for the exercises, I join every other textbook author in exhorting you to do them; but there is a further important point. In subjects such as number theory and combinatorics, some questions are simple to state but extremely hard to answer. Basic category theory is not like that. To understand the question is very nearly to know the answer. In most of the exercises, there is only one possible way to proceed. So, if you are stuck on an exercise, a likely remedy is to go back through each term in the question and make sure that you understand it in full. Take your time. Understanding, rather than problem solving, is the main challenge of learning category theory.

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