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34 votes
1 answer
5k views

Freyd-Mitchell's embedding theorem

Freyd–Mitchell's embedding theorem states that: if $A$ is a small abelian category, then there exists a ring R and a full, faithful and exact functor $F\colon A \to R\text{-}\mathrm{Mod}$. I have been ...
Bruno Stonek's user avatar
  • 3,004
15 votes
2 answers
2k views

When is bar-cobar duality an equivalence?

Let $A$ be an augmented differential graded algebra over a field $k$. I will write $BA$ for its bar construction (whose homology is $Tor^A(k, k)$). This is a co-augmented differential graded ...
Craig Westerland's user avatar
10 votes
1 answer
1k views

Is there a way to define a prime ideal object via diagrams in the category of rings?

I like to think in terms of commutative diagrams rather than referring to elements. So to me a group is really a group object, i.e. an object with some maps satisfying certain commutative diagrams. ...
David White's user avatar
  • 30.3k
5 votes
1 answer
367 views

Reference request: locally erasable delta-functor is universal

It is well-documented that an erasable delta-functor $(F^n,\delta)$ is universal. However, in 'small' abelian categories (in the technical sense or otherwise), there aren't always enough objects to ...
R. van Dobben de Bruyn's user avatar