Ziegler partial morphisms in additive exact categories

Abstract

We develop a general theory of partial morphisms in additive exact categories which extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact sequences in the category of modules over a ring. We relate partial morphisms with (co-)phantom morphisms and injective approximations and study the existence of such approximations in these exact categories.

Keywords

• ziegler partial morphism
• exact category
• injective hulls
• approximations