arXiv 1502.079292015-02-10math.CT

Two partial monoid structures on a set

Rachel A. D. Martins

备注：: Chapter in a wider investigation into double categories and C*-categories with Paolo Bertozzini and Roberto Conti. 10 pages

英文摘要：

It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent investigation into involutive double categories, we prove that a double category is equivalent to a set equipped with two partial monoid structures in which all structure maps $(s,t,\circ)$ are partial monoid homomorphisms. We discuss the light this purely algebraic perspective sheds on the symmetries of these structures and its applications. Iteration of the procedure leads also to a pure algebraic formulation of the notion of $n$-fold category.

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