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Results tagged with homological-algebra
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user 16785
(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.
1
vote
Localization of the injective hull
In Lemma 6 of Chapter 18 of 'Commutative ring theory' Matsumura proves the following.
Lemma: Let $A$ be a Noetherian ring, $S \subset A$ a multiplicative set, $M$ and $A$-module and $N \subset M$ a …
- 3,784
11
votes
Accepted
Reference for dualizable chain complexes
This is Proposition 1.6 of 'Duality, Trace and Transfer' by Dold and Puppe, http://www.maths.ed.ac.uk/~aar/papers/doldpup2.pdf.
- 3,784
3
votes
Accepted
A set of objects classically generates the full subcategory of compact objects iff it genera...
I agree that the various notions of 'generates' can be confusing. I think the following result may clarify what you are after (this can be found in Lemma 2.2.1 of 'Stable model categories are categori …
- 3,784