Nathaniel Stapleton

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20202026

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math.AT2026

Partition functors and universal exponential relations

David Mehrle, Millie Rose, Nathaniel Stapleton

We introduce partition functors: algebraic structures indexed by partitions of finite sets and equipped with restriction and transfer maps along refinements. We construct a monad P…

math.AT2026

Composition of bispans of $G$ -sets and plethysm

Nathan Cornelius, Evan Franchere, Usman Hafeez +4

Let $P (G)$ be the Grothendieck ring of the semiring of endomorphisms of the point in the $1$ -category of bispans of finite $G$ -sets for a finite group $G$ . This is the bispan analo…

Partition functors and universal exponential relations

Composition of bispans of G-sets and plethysm

Composition of bispans of $G$ -sets and plethysm