Symmetric Monoidal Categories with Attributes

Spencer Breiner
(National Institute of Standards and Technology)
John S. Nolan
(University of Maryland)

When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning, namely those based on symmetric monoidal categories and string diagrams. To accomplish this, we define a notion of a "symmetric monoidal category with attributes." This is a symmetric monoidal category in which objects are equipped with retrievable information and where the interactions between objects and information are governed by an "attribute structure." We discuss examples and semantics of such categories in the context of robotics to illustrate our definition.

In David Spivak and Jamie Vicary: Proceedings 3rd Annual International Applied Category Theory Conference 2020 (ACT 2020), Cambridge, USA, 6-10th July 2020, Electronic Proceedings in Theoretical Computer Science ??, pp. ??–??.
To appear.

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