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Embedding categories with exactness into their abelianization

Published online by Cambridge University Press:  09 April 2009

Murray Adelman
Murray Adelman
Affiliation:
Department of Mathematics, Macquarie University, N.S.W. 2113, Australia.
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Abstract

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We 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.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 275 - 283
Copyright
Copyright © Australian Mathematical Society 1977

References

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