TITLE: Embedding abelian categories to have enough projectives
QUESTION [6 upvotes]: Is it true that the pro-objects of an abelian category form a category with enough projectives? 
In general, given an abelian category A, is there a canonical way to embed it a bigger abelian category A' with enough projectives (or injectives) and such that A' is universal with respect to this property?

REPLY [3 votes]: It seems that Pro(A) does not have enough projectives in general. In Kashiwara-Schapira's book "Categories and Sheaves" they prove (corollary 15.1.3) that Ind(k-Mod) does not have enough injectives. This means, taking opposite categories, that Pro(k-Mod^{op}) does not have enough projectives.
I don't know of any universal way of adding enough projectives.