5
votes
1answer
416 views

permutation of projective limits with inductive limits

Hi everybody, I have a lack of references concerning projective limits and injective limits. Up to my faults in Bourbaki there are only proj and inj limits indexed by a partially ordered set (not a ...
10
votes
1answer
1k views

Is every ring the direct limit of Noetherian rings?

Are there any examples of commutative rings that do not occur as direct limits of Noetherian rings?
8
votes
2answers
1k views

Exactness of filtered colimits

Are filtered colimits exact in all abelian categories? In Set, filtered colimits commute with finite limits. The proof carries over to categories sufficiently like Set (i.e. where you can chase ...