Homological Algebra, by Charles Weibel

I have a lot of notes that I want to get out on the Internet. Hopefully, Google's trawlers eventually find them, and get this page catalogued by the search engine; and if someone happens to have a question about a missing detail in a proof that matches a detail I worked out here, and is able to artfully Google, then the twain shall meet.

I welcome constructive criticism of the stylistic layout, as long as you can actually tell me how to improve it. I am a bit clueless with the finer points of LaTeX, but I am always looking to learn.

http://www.math.wisc.edu/~nicodemus/Homological_Algebra_Weibel.pdf
http://www.math.wisc.edu/~nicodemus/Homological_Algebra_Weibel.tex

Comments

Post a Comment

Popular posts from this blog

Godement, Part IV - definition of monads, examples

A monad is a monoid in a category of endofunctors. In the previous post, we have established a very general notion of monoid which is suitable for many applications. For example, the category of chain complexes $R$-modules can be equipped with a monoidal product which associates to each pair $(C,C')$ of chain complexes the total complex $Tot(C\otimes C')$ of the double complex $(C\otimes C')_{i,j}= C_i\otimes C_j'$. The unit of this monoidal product is the complex with $R$ in dimension $0$ and $0$'s in all other dimension. A DG-algebra is precisely a monoid with respect to this monoidal product. For a given category $\mathcal{C}$, the functor category $[\mathcal{C};\mathcal{C}]$ is naturally equipped with thestructure of a strict monoidal category, whose monoidal product $\otimes$ is precisely functor composition, $F\otimes G= F\circ G$; and whose unit $1$ is precisely the identity functor $id_{\mathcal{C}}$. It is easily verified that this is functorial simulta...
Read more

Monads or triples?

From my own reading it seems that monad is more common in general but triple does seem to continue to live on in the homological algebra community. Barr and Beck both continue to use it. I found their paper "Acyclic Models and Triples" to be very enlightening - such a simple idea. I am working with a CS advisor who studies connections between category theory and programming languages. Computer scientists have found it useful to use monads to structure sequential composition of programs, so monads come up a lot there - see Moggi's "Notions of Computations and Monads". Really, a lot of the reason I am learning homological algebra is to understand the purpose and meaning of these "canonical resolutions." I am picking up French a little at a time to read the book by Godement, which is excellent. His goal in the book is to cover the homology theory of simplicial sets and simplicial complexes, briefly cover spectral sequences, and cover t...
Read more

A response to an undergrad - What do I study?

An undergrad that I was a T.A. for recently asked me what my research is in. I decided to write up an answer as a blog post, in a way that is accessible to the average early undergrad student in STEM. I study logic. More specifically, I study semantics. In linear algebra, you start off with a certain formal algebraic language, the language of vector spaces - it has certain distinguished constant symbols you are permitted to use, like "0" for the zero vector, or any real number; you are permitted to use variables v, w, ... that range across the vectors; there are also special symbols that represent functions, like "+", for addition. There are also certain axioms, written in the language. One also has a list of formal logical laws that allow you to combine the axioms in various ways to derive theorems in the theory of linear algebra. Linear algebra from this point of view is the collection of all formal statements in the language of linear algebra that c...
Read more