Directed Containers as Categories
arXiv:1604.01187 · doi:10.4204/EPTCS.207.5
Abstract
Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a directed container morphism those of a monoid morphism in the reverse direction. With some reorganization, a directed container is the same as a small category, but a directed container morphism is opcleavage-like. We draw some conclusions for comonads from this observation, considering in particular basic constructions and concepts like the opposite category and a groupoid.
In Proceedings MSFP 2016, arXiv:1604.00384