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Apr
8
comment Why are functors exact if they preserve all short exact sequences?
At the end of this answer to a related question, I post a link to something I wrote up (in Spanish) which contains exactly what you want. If you understand it and write it up in English and post it as an answer, I'd upvote it :)
Apr
7
revised Computation of $Ext^*_R(k,k)$ as an algebra using a dga-resolution
edited tags
Apr
6
revised Duality between Tor and Ext?
added 28 characters in body
Apr
6
comment Classification of finitely generated multigraded modules over $K[x_1,\ldots,x_n]$?
Why the hell does this have a -3 vote count? (-2 now). Sometimes I really don't understand math.SE user's vote patterns.
Apr
6
answered Duality between Tor and Ext?
Apr
6
comment Ring structure on $Ext$ and $Tor$
Found another reference: Mac Lane's Homology, section VIII (Products). There's also Cartan & Eilenberg which is really comprehensive and immensely general. And I'm going to leave a link to a question I just asked here, because it is somehow related and I think it would be useful to have them formally linked: math.stackexchange.com/questions/1222604/… .
Apr
6
asked Computation of $Ext^*_R(k,k)$ as an algebra using a dga-resolution
Apr
6
comment Reference request: extending tensor product of modules
Do you want a reference where it is used (it's used all over the place!), as you say, or do you want a reference where it is explained? If it's the latter, try KConrad's two blurbs on tensor products, they are very nice. It's called "extension of scalars" or "base change", usually.
Mar
31
comment Explicit example of Koszul complex
Do you have a reference for the content of your post? Thanks.
Mar
31
comment How to compute Ext over an exterior algebra
Also, this question is definitely related, if not almost a duplicate: math.stackexchange.com/questions/366927/…
Mar
30
comment How to compute Ext over an exterior algebra
You should look at Lang's Algebra, almost at the end of the book: it's p. 861 in my edition.
Mar
29
comment Ring structure on $Ext$ and $Tor$
You should check these notes by May: math.uchicago.edu/~may/MISC/TorExt.pdf
Mar
11
comment Why the whole exterior algebra?
I am tempted to give the following application: exterior algebras are important because they are particular cases of Clifford algebras which are important in full, not just their homogeneous coordinates, for example in constructing the Atiyah-Bott-Shapiro isomorphism (aka algebraic Bott periodicity). But I'm not comfortable enough with these concepts to post this as an answer, and it is stretching it a bit (ABS theorem does not consider trivial Clifford algebras, i.e. exterior algebras).
Mar
11
comment Why the whole exterior algebra?
I sympathize with your answer, which is the same thing I thought when I read the question, but that still doesn't say why it would be useful to consider the whole graded algebra and not just its homogeneous components separately...
Mar
11
comment Is There a de Rham Homology
See mathoverflow.net/questions/16657/de-rham-homology
Mar
9
answered Spin structures, frame bundles, and trivializations over the 2-skeleton
Feb
26
awarded  Tumbleweed
Feb
19
revised Obstruction theory for homotopies
added 93 characters in body
Feb
19
asked Obstruction theory for homotopies
Feb
5
awarded  Nice Question