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Results tagged with abelian-categories
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user 6936
1
vote
Mitchell's embedding theorem
EDIT: I'm completely rewriting this in detail now that I think I've worked it out. Lots of possibilities for mistakes here, so stay alert!
I claim that the generalization to include $(a)$ fails. My c …
- 13.5k
35
votes
Abelian category equivalent to a non-abelian category
Here is a manifestly invariant definition of an abelian category $\mathcal{C}$. It is a category with finite limits and colimits such that:
(It is pointed) the map from the initial to the final obje …
- 13.5k
9
votes
how to make the category of chain complexes into an $(\infty,1)$-category
I don't know what 'explicit' means, but this is all covered in Higher Algebra very well.
If you want a simplicial category at the end of the day, you can either...
Take your favorite $\infty$-categ …
- 13.5k