Directed Containers as Categories
Logic in Computer Science
2016-05-06 v1 Programming Languages
Category Theory
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.
Keywords
Cite
@article{arxiv.1604.01187,
title = {Directed Containers as Categories},
author = {Danel Ahman and Tarmo Uustalu},
journal= {arXiv preprint arXiv:1604.01187},
year = {2016}
}
Comments
In Proceedings MSFP 2016, arXiv:1604.00384