Schur Functors and Categorified Plethysm

Reference. Schur Functors and Categorified Plethysm

John C. Baez, Joe Moeller, Todd Trimble · arXiv · 2021 · category-theory · arXiv

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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Cite as @baez-2021-schur (helia, typst) · \cite{baez-2021-schur} (LaTeX)

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bibtex · 8 lines

@misc{baez-2021-schur,
  author = {John C. Baez and Joe Moeller and Todd Trimble},
  title = {Schur Functors and Categorified Plethysm},
  year = {2021},
  month = {6},
  eprint = {2106.00190},
  archiveprefix = {arXiv}
}

hayagriva YAML (typst)

yaml · 10 lines

baez-2021-schur:
  type: misc
  title: Schur Functors and Categorified Plethysm
  author:
  - Baez, John C.
  - Moeller, Joe
  - Trimble, Todd
  date: 2021-06
  serial-number:
    arxiv: '2106.00190'

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Two-dimensional monad theory blackwell_kelly_power_1989JPAA · 1989

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