Products in a Category with One Object

Aaron Gray; Keith Pardue

Products in a Category with One Object

Category Theory 2016-08-23 v2 Combinatorics

Authors: Aaron Gray , Keith Pardue

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 $X$ .

Keywords

monoidal category theory monoids category theory and monads

Cite

@article{arxiv.1604.03999,
  title  = {Products in a Category with One Object},
  author = {Aaron Gray and Keith Pardue},
  journal= {arXiv preprint arXiv:1604.03999},
  year   = {2016}
}

Comments

This is a revised version of the paper first posted in April. We have tightened some arguments and added a new section with a conjecture and some further questions. Please send comments to the second author

Products in a Category with One Object

Abstract

Keywords

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