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(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.

2 votes
0 answers
101 views

Existence of a certain derived functor

This is a sequel to this question. Let $k$ be a field, let $A$ be the $k$-algebra $k[\varepsilon]$ with $\varepsilon^2=0$, and consider the following three abelian categories: $\bullet\ \text M(A)$ …
20 votes
1 answer
970 views

Example of an additive functor admitting no right derived functor

I asked the same question a week ago on Mathematics Stackexchange but got no answer. What would be a simple example of an additive functor $F:\mathcal C\to\mathcal C'$ of abelian categories such that …
4 votes
1 answer
543 views

Generators of a certain ideal

In view of Mariano Suárez-Alvarez's answer I see how badly phrased my question was, and decided to rewrite it. The drawback is that some comments of Martin Brandenburg are now incomprehensible, but I …
17 votes
Accepted

"Sums-compact" objects = f.g. objects in categories of modules?

It seems to me the references in this Mathematics - Stack Exchange answer contain the requested information. EDIT 1. Here is an excerpt from Hyman Bass's book Algebraic K-Theory, W. A. Benjamin (196 …
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