Polynomial Functors: A Mathematical Theory of Interaction
Nelson Niu, David I. Spivak
TL;DR
This paper develops a categorical framework using polynomial endofunctors to model interaction protocols and dynamical systems, emphasizing pictorial techniques and concrete examples for intuition.
Contribution
It introduces a comprehensive categorical theory of polynomial endofunctors applied to interaction modeling, with new pictorial methods and practical applications.
Findings
Categorical framework for interaction protocols
Pictorial techniques for polynomial functors
Applications to dynamical systems
Abstract
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical theory from the ground up, highlighting pictorical techniques and concrete examples to build intuition and provide applications.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Constraint Satisfaction and Optimization