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arXiv · 2106.00190

Schur Functors and Categorified Plethysm

John C. Baez·Joe Moeller·Todd Trimble
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Abstract

It is known that the Grothendieck group of the category of Schur functors is the ring of symmetric functions. This ring has a rich structure, much of which is encapsulated in the fact that it is a "plethory": a monoid in the category of birings with its substitution monoidal structure. We show that similarly the category of Schur functors is a "2-plethory", which descends to give the plethory structure on symmetric functions. Thus, much of the structure of symmetric functions exists at a higher level in the category of Schur functors.

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John C. Baez, Joe Moeller, Todd Trimble. 2021-06-01. Schur Functors and Categorified Plethysm. https://arxiv.org/abs/2106.00190

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