Weakly polynomial functors
Aur\'elien Djament (LMJL), Christine Vespa (IRMA)

TL;DR
This paper introduces a broad concept of polynomial functors within symmetric monoidal categories with initial units, providing a classification for those up to a certain degree in the context of hermitian spaces.
Contribution
It defines and studies a general notion of polynomial functors and classifies them in the setting of hermitian spaces for degrees up to n.
Findings
Classification of polynomial functors of degree ≤ n in hermitian spaces
Introduction of a general framework for polynomial functors in symmetric monoidal categories
Establishment of a hierarchy of polynomial functors by degree
Abstract
We introduce and study a general notion of polynomial functor from a small monoidal symmetric category whose unit is an initial object and give a classification result of polynomial functors of degree smaller of equal to n modulo those of degree smaller of equal to n-1 in the case of a category of hermitian spaces.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
