An Internal Language for Autonomous Categories
In this extended abstract we present an internal language for symmetric monoidal closed (autonomous) categories analogous to the typed lambda calculus being an internal language for cartesian closed categories. The language we propose is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous theory. We prove that this language is an internal language and show as an application the coherence theorem of Kelly and Mac Lane, which becomes straightforward to state and prove. We then hint at some further applications of this language; a further treatment will be given in the full paper.
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