I ~ I ~ is A-inJective. ,p, > Ii for A-inJective of (*) A' H~ ") in I ~ ) 60b A' which is possible since I~ p, and choose I p+I to be an containing IP/im i p-I ~ zP+I(x ") . Xp We must check that this latter is in A'. subcategory, Indeed, A' is a thick so it is sufficient to note that IP/im I p-I 6 A' (one shows by induction that Bi(I" ) and zi(I" ) for all i), and that the quotient of (*) by HP+I(x'), which is in A' by hypothesis.
Algebraic geometry : introduction to schemes by I.G. Macdonald