2015/02/10 by Martins, Rachel A. D.
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1502.07929
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,∘) 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.