  We study the question when a category of ind-objects is abelian. Our answer
allows a further generalization of the notion of weakly Tannakian categories
introduced by the author. As an application we show that, under suitable
conditions, the category of coherent sheaves on the product of two schemes with
the resolution property is given by the Deligne tensor product of the
categories of coherent sheaves of the two factors. To do this we prove that the
class of quasi-compact and semi-separated schemes with the resolution property
is closed under fiber products.
