Todd Trimble
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View article: Tannaka Reconstruction and the Monoid of Matrices
Tannaka Reconstruction and the Monoid of Matrices Open
Settling a conjecture from an earlier paper, we prove that the monoid $\mathrm{M}(n,k)$ of $n \times n$ matrices in a field $k$ of characteristic zero is the "walking monoid with an $n$-dimensional representation". More precisely, if we tr…
View article: 2-Rig Extensions and the Splitting Principle
2-Rig Extensions and the Splitting Principle Open
Classically, the splitting principle says how to pull back a vector bundle in such a way that it splits into line bundles and the pullback map induces an injection on $K$-theory. Here we categorify the splitting principle and generalize it…
View article: Differential 2-rigs
Differential 2-rigs Open
We study the notion of a "differential 2-rig", a category R with coproducts and a monoidal structure distributing over them, also equipped with an endofunctor D : R -> R that satisfies a categorified analogue of the Leibniz rule. This is i…
View article: Schur Functors and Categorified Plethysm
Schur Functors and Categorified Plethysm Open
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 bi…