## Is an abelian category a Serre subcategory of its ind-category?

Let C be an abelian category and consider its ind-category Ind(C): (1) Is Ind(C) always abelian? (If not, what conditions are needed?) (2) Is C⊆Ind(C) a Serre subcategory? In other words, if we have a short exact sequence: 0⟶M′⟶M⟶M″ in Ind(\mathcal C), then M\in \mathcal C iff M’ and M” are in \mathcal C? Answer … Read more