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Container Combinatorics: Monads and Lax Monoidal Functors

Abstract : Abbott et al.’s containers are a “syntax” for a wide class of set functors in terms of shapes and positions. Containers whose “denotation” carries a comonad structure can be characterized as directed containers, or containers where a shape and a position in it determine another shape, intuitively a subshape of this shape rooted by this position. In this paper, we develop similar explicit characterizations for container functors with a monad structure and container functors with a lax monoidal functor structure as well as some variations. We argue that this type of characterizations make a tool, e.g., for enumerating the monad structures or lax monoidal functors that some set functor admits. Such explorations are of interest, e.g., in the semantics of effectful functional programming languages.
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Tarmo Uustalu. Container Combinatorics: Monads and Lax Monoidal Functors. 2nd International Conference on Topics in Theoretical Computer Science (TTCS), Sep 2017, Tehran, Iran. pp.91-105, ⟨10.1007/978-3-319-68953-1_8⟩. ⟨hal-01760638⟩

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