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arXiv · 1604.01187

Directed Containers as Categories

Danel Ahman·Tarmo Uustalu
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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.

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Danel Ahman, Tarmo Uustalu. 2016-04-05. Directed Containers as Categories. https://doi.org/10.4204/eptcs.207.5

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