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Handbook of Categorical Algebra: Volume 1, Basic Category Theory (Encyclopedia of Mathematics and its Applications) epub

by Francis Borceux


Handbook of Categorical Algebra: Volume 1, Basic Category Theory (Encyclopedia of Mathematics and its Applications) epub

ISBN: 0521061199

ISBN13: 978-0521061193

Author: Francis Borceux

Category: Science

Subcategory: Mathematics

Language: English

Publisher: Cambridge University Press; 1 edition (April 24, 2008)

Pages: 364 pages

ePUB book: 1505 kb

FB2 book: 1584 kb

Rating: 4.9

Votes: 505

Other Formats: mbr lit azw rtf





Handbook of Categorical Algebra book. Goodreads helps you keep track of books you want to read

Handbook of Categorical Algebra book. Goodreads helps you keep track of books you want to read. Start by marking Handbook of Categorical Algebra: Volume 1, Basic Category Theory (Encyclopedia of Mathematics and its Applications) (v. 1) as Want to Read: Want to Read savin. ant to Read.

As such it will be a unique reference. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.

Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations.

Volume 1: Basic Category Theory. As such it will be a unique reference

Volume 1: Basic Category Theory. Online ISBN: 9780511525858. As such it will be a unique reference. Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.

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Handbook of Categorical Algebra" by Francis Borceux (V. 1, 2008) (V. 2, 1995) . 1, Encyclopedia of Mathematics and its Applications, vol. Basic category theory. Category theory ultimately seems very. 2, 1995) (v. As a consequence, the space of unital associative algebra structures on a given object is up to (5) Francis Borceux, Handbook of categorical algebra. Category theory is the key to a clear presentation of modern abstract "Basic Category Theory for Computer Scientists" by Benjamin C. Pierce (1991). Category theory ultimately seems ver. ONTINUE READING.

Handbook of Categorical Algebra (Encyclopedia of Mathematics and its Applications) by Francis Borceux. This site has 18 books and articles on category theory in PDF, including several by . This is NOT free, but you can see the pts at the publisher's web site, listed below. Abstract and Concrete Categories-The Joy of Cats by Jirı Adamek, Horst Herrlich, and George E. Strecker (524pp). Free PDF. Published under the GNU Free Documentation License.

Linear Algebra Books. This button opens a dialog that displays additional images for this product with the option to zoom in or out. Report incorrect product info or prohibited items. Handbook of Categorical Algebra : Volume 1, Basic Category Theory. Volume 1 covers basic concepts. Handbook of Categorical Algebra: Volume 1, Basic.

A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various "refinements" of the fundamental concepts of category and functor.
perfect!
The Yoneda lemma is something experts will tell you follows trivially from definitions, while the beginner may struggle to get ahold of it. Mac Lane helpfully provides a single diagram and states "The proof is indicated by the following commutative diagram". The naturality conditions are brushed aside as self-evident. I struggled quite a bit with this proof when I first saw it. By contrast, Borceux provides Mac Lane's diagram, but adds nearly three pages worth of detail to his proof. Some people may see this as overkill, but it's wonderful to anyone trying to get accustomed to the language of category theory.

That's what I really appreciate from Borceux (in contrast from Mac Lane and others) - the level of detail he provides. The text is absolutely littered with examples, and most of them are recurring themes - sets, modules, vector spaces, (abelian) groups, banach spaces, rings, topological spaces, compact hausdorff spaces. (You won't need familiarity with all of these to read the book, but since examples are such a huge part, I strongly recommend knowing most of those if you want to read Borceux. They're about all the book asks for as far as prerequisites.) Very rarely does he leave important details as an "exercise for the reader". Not everything is easy, I'll readily admit the final two chapters were a bit too dizzying for me to get a good handle on, but that's the nature of the subject. Learning category theory is hard no matter what course you take, but Borceux's first handbook is the best place to begin that I know of.

There are a few drawbacks - my biggest complaint is that his treatment of kan extensions was not thorough enough - they still seem like a mystery gadget to me. There are also a few proofs that have major flaws or are just silly. (For example, 4.4.5(3) follows directly from the definition of strong-epic, so a diagram and five-line proof citing earlier results is completely unnecessary.)

I'm excited to move on to book 2. I'm hoping it's just as good as this one.
I used this book after making several attempts to finding a good introductory text for self study.

I tried Mac Lane, Awodey, Pareigis, and a few others (there are a dozen at my library that I have tried) this is the first one that I could actually sit down and fully appreciate the fundamentals of category theory in a rigorous perspective. I do recommend it for self study.

However, there are some drawbacks. Though it requires little background to approach, the disadvantage of that is that the examples are limited. Also, his formulations aren't always the best for learning but more for reference (especially the commutativity of limits.) but overall it was the most beneficial for me to learn from.

Now I study from Mac Lane and other books on special topics, but I keep Borceux still because it's an amazing reference book on anything found under the topics of its chapters. I still use it when studying any other text in category theory.