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We introduce the notions of premonoidal category and premonoidal functor, and show how these can be used in the denotational semantics of programming languages. We characterize the semantic definitions of Eugenio Moggi's monads as notions of computation, exhibit a representation theorem for our premonoidal setting in terms of monads, and give a fibrational setting for the structure.
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Power et al. (1997) studied this question.
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