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arXiv · 1709.06971

New Examples of Dimension Zero Categories

Andrew Gitlin
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Abstract

We say that a category $\mathscr{D}$ is dimension zero over a field $F$ provided that every finitely generated representation of $\mathscr{D}$ over $F$ is finite length. We show that $\textrm{Rel}(R)$, 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 $\textrm{Rel}$, the category of finite sets with relations, is dimension zero over any infinite field.

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Andrew Gitlin. 2017-09-20. New Examples of Dimension Zero Categories. https://doi.org/10.1016/j.jalgebra.2018.03.009

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