Abstract
This paper is about a categorical approach to model a simple term calculus, named S�λ - calculus. This is the core calculus underlying the programming language SPCF that have been conceived in order to program only linear functions between Coherence Spaces. In this work, we introduce the notion of S�λ -category, which is able to describe a large class of sound models of S�λ -calculus. S�λ -category extends in the natural way Benton, Bierman, Hyland and de Paiva's Linear Category. We will define two interpretations of S�λ -calculus types and terms into objects and morphisms of S�λ -categories: the first one is a generalization of the translation given in (18) but lacks in completeness; the second one uses the comonadic properties of ! to recover completeness. Finally, we show that this notion is general enough to catch interesting models in Scott Domains and Coherence Spaces.
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