Decorated Corelations

نویسنده

  • Brendan Fong
چکیده

Let C be a category with finite colimits, and let (E ,M) be a factorisation system on C with M stable under pushouts. Writing C;M for the symmetric monoidal category with morphisms cospans of the form c → m ←, where c ∈ C and m ∈ M, we give method for constructing a category from a symmetric lax monoidal functor F : (C;M,+) → (Set,×). A morphism in this category, termed a decorated corelation, comprises (i) a cospan X → N ← Y in C such that the canonical copairing X + Y → N lies in E , together with (ii) an element of FN . Functors between decorated corelation categories can be constructed from natural transformations between the decorating functors F . This provides a general method for constructing hypergraph categories— symmetric monoidal categories in which each object is a special commutative Frobenius monoid in a coherent way—and their functors. Such categories are useful for modelling network languages, for example circuit diagrams, and such functors their semantics.

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عنوان ژورنال:
  • CoRR

دوره abs/1703.09888  شماره 

صفحات  -

تاریخ انتشار 2017