• Corpus ID: 235265922

Schur Functors and Categorified Plethysm

@inproceedings{Baez2021SchurFA,
  title={Schur Functors and Categorified Plethysm},
  author={John C. Baez and Joe Moeller and Todd Trimble},
  year={2021}
}
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… 
Differential 2-rigs
We propose the notion of differential 2-rig, a category R equipped with coproducts and a monoidal structure distributing over them, also equipped with an endofunctor m : R → R that satisfies a

References

SHOWING 1-10 OF 38 REFERENCES
Monoidal Bicategories and Hopf Algebroids
Why are groupoids such special categories? The obvious answer is because all arrows have inverses. Yet this is precisely what is needed mathematically to model symmetry in nature. The relation
Tall-Wraith Monoids
Tall‐Wraith monoids were introduced in [SW09] to describe the algebraic structure on the set of unstable operations of a suitable generalised cohomology theory. In this paper we begin the study of
Ind-abelian categories and quasi-coherent sheaves
We study the question when a category of ind-objects is abelian. Our answer allows a further generalization of the notion of weakly Tannakian categories introduced by the author. As an application we
Representable Functors and Operations on Rings
Introduction The main aim of this article is to describe the mechanics of certain types of operations on rings (e.g. A-operations on special A-rings or differentiation operators on rings with
The cartesian closed bicategory of generalised species of structures
The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of
ON BIADJOINT TRIANGLES
We prove a biadjoint triangle theorem and its strict version, which are 2-dimensional analogues of the adjoint triangle theorem of Dubuc. Similarly to the 1-dimensional case, we demonstrate how we
Supplying bells and whistles in symmetric monoidal categories.
It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in
...
...