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Results tagged with homological-algebra
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user 32022
(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.
8
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2
answers
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Properties of quotient categories.
I asked this on math.stackexchange.com, but didn't get any answer.
Let $\mathcal{A}$ be an abelian category and $\mathcal{C}$ a localizing subcategory in the sense of Gabriel. (A Serre/thick/dense su …
CommunityBot
- 1
6
votes
Why is $Lex(\mathcal{A},\mathcal{Ab})$ abelian? Does $Lex(\mathcal{A},\mathcal{Ab})\rightarr...
Almost all of your questions are answered in Pierre Gabriel's dissertation "Des catégories abéliennes".
He shows in a more general case, that the left exact functors between nice abelian categories a …
- 2,974
10
votes
1
answer
923
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Examples of applications of the Freyd-Mitchell embedding theorem.
The Freyd-Mitchell embedding theorem states the following:
Let $\mathcal{A}$ be a small abelian category. There exists a unital ring $R$ and a full, faithful and exact functor $F\colon\mathcal{A}\ …
- 56.9k