Homological Algebra texts - MathOverflow

Homological Algebra texts

2009-10-25T23:37:37Z

I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe).

As usual, the rule is one reference per post. Please include some description which distinguishes it from other texts.

Answer by Andreas Holmstrom for Homological Algebra texts

2009-10-26T00:31:12Z

A less well-known book is Vermani: An elementary approach to homological algebra. This was the first book I ever read on homological algebra, and I loved it. I would recommend it to anyone who has not seen much of the subject, as a starting point before going on to more advanced texts. Here is a Google Books preview.

Answer by Andreas Holmstrom for Homological Algebra texts

2009-10-26T00:38:30Z

There are two books by Gelfand and Manin, Homological algebra, around 200 pages and Methods of homological algebra, around 350 pages. The first one covers the standard basic topics, and also has chapters on mixed Hodge structures, perverse sheaves, and D-modules. The second one has a different emphasis, with chapters on simplicial sets and homotopical algebra instead of the above-mentioned topics.

Answer by Andreas Holmstrom for Homological Algebra texts

2009-10-26T00:41:43Z

It seems difficult to find good introductions that are freely available online, but a nice set of lecture notes can be be found on Schapira's web page, here.

Answer by Akhil Mathew for Homological Algebra texts

2009-10-26T00:45:27Z

There's a basic book by Northcott; it does everything only for the category of modules over a ring and does not go far, but it has essentially no prerequisites.

It was written soon after Cartan and Eilenberg, which probably explains the old-fashioned style.

Answer by Andrew L for Homological Algebra texts

2010-03-13T07:38:44Z

Charles Weibel's "An Introduction To Homological Algebra" is the gold standard. Very modern, very clear and written by a master. But it may be a bit rough going for beginners. Much more user friendly and still very thorough is the second edition of Joseph Rotman's book of the same name. Like everything by Rotman, it's a wonderful and enlightening read.

Answer by Saikat Biswas for Homological Algebra texts

2011-06-27T23:58:44Z

Part IV of Lang's 'Algebra', especially Chapter XX, covers almost everything you want to learn about homological algebra in a first course.

Answer by Hicham YAMOUL for Homological Algebra texts

2011-06-29T12:42:20Z

There is also an interesting lectures on homological algebra of I.Moerdijk, which his notes are on the following link http://www.staff.science.uu.nl/~lukac101/homalg2007.pdf

Answer by Blah for Homological Algebra texts

2011-06-29T13:50:27Z

I liked Rotmans book a lot.

http://www.amazon.com/Introduction-Homological-Algebra-Universitext/dp/0387245278

Answer by Graham Denham for Homological Algebra texts

2011-11-10T15:46:02Z

I have used Weibel in the past as my reference in a graduate course, but I think the less confident students can have trouble getting into it. I've always enjoyed the way it is organized, somehow. The books by Rotman and Scott Osborne (Basic Homological Algebra) seem friendlier for students, but I like to have spectral sequences early on, not just in the last chapter. (Who likes to balance Tor by hand?)

Answer by IDoHomologicalAlgebra for Homological Algebra texts

2012-05-02T12:49:05Z

I agree the best reference is Weibel, and GM's Methods is really good, but for starting out I'd recommend Mac Lane's Homology (which is just about homological algebra). This is much more readable for someone coming from an undergraduate degree.

Answer by Jake for Homological Algebra texts

2012-05-02T13:12:39Z

Basic Homological Algebra by Scott Osbourne is a nice beginners text. It is very thorough and detailed yet well motivated and conversational with a particularly engaging style.

Although old fashioned and outdated in many respects; I would have to say that Cartan-Eilenberg is still of great value as a reference.