DeepAI AI Chat
Log In Sign Up

Symmetric Monoidal Categories with Attributes

by   Spencer Breiner, et al.

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.


page 1

page 2

page 3

page 4


String diagrams for symmetric powers I: In symmetric monoidal ℚ_≥ 0-linear categories

Symmetric powers are an important notion in mathematics, computer scienc...

Nominal String Diagrams

We introduce nominal string diagrams as, string diagrams internal in the...

Wiring diagrams as normal forms for computing in symmetric monoidal categories

Applications of category theory often involve symmetric monoidal categor...

Coinductive Streams in Monoidal Categories

We introduce monoidal streams. Monoidal streams are a generalization of ...

Evaluating Linear Functions to Symmetric Monoidal Categories

A number of domain specific languages, such as circuits or data-science ...

Dilations and information flow axioms in categorical probability

We study the positivity and causality axioms for Markov categories as pr...

*-autonomous envelopes and 2-conservativity of duals

We show the doctrine of ∗-autonomous categories is "2-conservative" over...