Int Construction and Semibiproducts

We study a relationship between the Int construction of Joyal et al. and a weakening of biproducts called semibiproducts. We then provide an application of geometry of interaction interpretation for the multiplicative additive linear logic (MALL for short) of Girard. We consider not biproducts but semibiproducts because in general the Int construction does not preserve biproducts. We show that Int construction is left biadjoint to the forgetful functor from the 2category of compact closed categories with semibiproducts to the 2-category of traced symmetric monoidal categories with semibiproducts. We then illustrate a traced distributive symmetric monoidal category with biproducts B(Pfn) and relate the interpretation of MALL in Int(B(Pfn)) to token machines defined over weighted MALL proofs.

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