منابع مشابه
Directed Containers as Categories
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 catego...
متن کاملCategories of containers
We introduce the notion of containers as a mathematical formalisation of the idea that many important datatypes consist of templates where data is stored. We show that containers have good closure properties under a variety of constructions including the formation of initial algebras and final coalgebras. We also show that containers include strictly positive types and shapely types but that th...
متن کاملDistributive Laws of Directed Containers
Containers [1] are an elegant representation of a wide class of datatypes in terms of shapes and positions in shapes. In our FoSSaCS 2012 work [2], we introduced directed containers as a special case to account for the common situation where every position in a shape determines another shape, informally the subshape rooted by that position; some examples being the datatypes of nonempty lists an...
متن کاملUpdate Monads: Cointerpreting Directed Containers
Containers are a neat representation of a wide class of set functors. We have previously [1] introduced directed containers as a concise representation of comonad structures on such functors. Here we examine interpreting the opposite categories of containers and directed containers. We arrive at a new view of a di↵erent (considerably narrower) class of set functors and monads on them, which we ...
متن کاملDirected Algebraic Topology, Categories and Higher Categories
Directed Algebraic Topology is a recent field, deeply linked with Category Theory. A ‘directed space’ has directed homotopies (generally non reversible), directed homology groups (enriched with a preorder) and fundamental n-categories (replacing the fundamental ngroupoids of the classical case). On the other hand, directed homotopy can give geometric models for lax higher categories. Applicatio...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2016
ISSN: 2075-2180
DOI: 10.4204/eptcs.207.5