New Examples of Dimension Zero Categories

Abstract

We say that a category $\mathcal{D}$ is dimension zero over a field $F$ provided that every finitely generated representation of $\mathcal{D}$ over $F$ is finite length. We show that $\text{Rel}(R)$, a category that arises naturally from a finite idempotent semiring $R$, is dimension zero over any infinite field. One special case of this result is that $\text{Rel}$, the category of finite sets with relations, is dimension zero over any infinite field.

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References in corpus (1)

• The representation theory of finite sets and correspondences