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3 - The category of polynomial functors

from Part I - The category of polynomial functors

Published online by Cambridge University Press:  aN Invalid Date NaN

Nelson Niu
Affiliation:
University of Washington
David I. Spivak
Affiliation:
Topos Institute
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Summary

We define the category of polynomial functors by introducing its morphisms, called dependent lenses or lenses for short, and we show how they model interaction protocols. We introduce several methods for working with these lenses, including visual tools such as corolla forests and polybox pictures. We explain how these lenses represent bidirectional communication between polynomials and describe how they compose. By the end of the chapter, readers will have a comprehensive understanding of how polynomial functors and their morphisms can be used to model complex interactive behaviors.

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Chapter
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Polynomial Functors
A Mathematical Theory of Interaction
, pp. 51 - 104
Publisher: Cambridge University Press
Print publication year: 2025

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