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10 votes
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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}\ …
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8 votes
2 answers
2k views

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 …
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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 …
archipelago's user avatar
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