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arXiv · 1604.03999

Products in a Category with One Object

Aaron Gray·Keith Pardue
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Abstract

We study monoids equipped with a second binary operation that captures the structure of the endomorphisms of an object $X$ such that $X=X\times X$. We construct a universal monoid of this type and examine some of its rich combinatorial structure. We show that if $X$ has a nontrivial endomorphism and $X=X\times X$, then every finite monoid has a faithful action on $X$.

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Aaron Gray, Keith Pardue. 2016-08-19. Products in a Category with One Object. https://arxiv.org/abs/1604.03999

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