Relevant Categories and Partial Functions

Kosta Došen, Zoran Petrić

A relevant category is a symmetric monoidal closed category with a diagonal natural transformation that satisfies some coherence conditions. Every cartesian closed category is a relevant category in this sense. The denomination \emph{relevant} comes from the connection with relevant logic. It is shown that the category of sets with partial functions, which is isomorphic to the category of pointed sets, is a category that is relevant, but not cartesian closed.