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The subject of linear logic has recently become very important in theoretical computer science. It is apparent that the *-autonomous categories studied at length in by Barr (1979) are a model for a large fragment of linear logic, although not quite for the whole thing. Since the main reference is out of print and since large parts of that volume are devoted to results highly peripheral to the matter at hand, it seemed reasonable to provide a short introduction to the subject.
Michael Barr (Mon,) studied this question.