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Product Systems Over Right-Angled Artin Semigroups, Neal J. Fowler, Aidan Sims

Faculty of Engineering and Information Sciences - Papers: Part A

We build upon MacLane's definition of a tensor category to introduce the concept of a product system that takes values in a tensor groupoid G. We show that the existing notions of product systems fit into our categorical framework, as do the k-graphs of Kumjian and Pask. We then specialize to product systems over right-angled Artin semigroups; these are semigroups that interpolate between free semigroups and free abelian semigroups. For such a semigroup we characterize all product systems which take values in a given tensor groupoid G. In particular, we obtain necessary and sufficient conditions under which a collection of …

A Classification Of Intersection Type Systems, Martin W. Bunder

Faculty of Engineering and Information Sciences - Papers: Part A

The first system of intersection types. Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules ((ΛI ) and (ΛE) ) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction.

Urzyczyn proved in [6] that for both these systems it is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] …