Take the 2-minute tour ×  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?  share|improve this question Matthew Emerton's
answer
sbseminar.wordpress.com/2009/09/10/20-questions/#comment-6499 to
question 14 would be worth looking at. –  Greg Stevenson Oct 17
'09 at 7:26 Thanks! Do you have a reference for the proof? – 
Akhil Mathew Oct 18 '09 at 3:40  2 Answers 2  up vote 2 down
vote accepted  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.  share|improv