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Results tagged with abelian-categories
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user 32022
10
votes
1
answer
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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}\ …
- 2,974
8
votes
2
answers
2k
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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 …
- 2,974
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