EXACT CATEGORIES AND VECTOR SPACE CATEGORIES

with an appendix by B. KELLER Abstract. In a series of papers starting with [ASo] additive subbifunctors F of the bifunctor Ext ( ; ) are studied in order to establish a relative homology theory for an artin algebra . On the other hand, one may consider the elements of F (X;Y) as short exact sequences. We observe that these exact sequences make mod into an exact category if and only if F is closed in the sense of [BH]. Concerning the axioms for an exact category we refer to [GR]. In fact, for our general results we work with subbifunctors of the extension functor for arbitrary exact categories. In order to study projective and injective objects for exact categories it turns out to be convenient to consider categories with almost split exact pairs because many of the results from [ASo] can easily be adapted to this situation. Exact categories arise in representation theory for example if one stud-ies categories of representations of bimodules. Representations of bimodule