Abstract
AbstractWe give a partial answer to the following questions: Given an additive category and a class of sequences, under what conditions is the universal functor to the abelian category faithful and what other sequences are taken to exact sequences?The “answers” to these questions appear as theorems 2.2 and 3.2 respectively and amount to a weakening of the condition that there be enough relative projectives.We then characterize those additive categories with exactness which have the property that all relative exact sequences are determined by a small set of functors into the category of abelian groups.
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