Container combinatorics: Monads and lax monoidal functors

Tarmo Uustalu*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationTopics in Theoretical Computer Science
Subtitle of host publication2nd IFIP WG 1.8 International Conference, TTCS 2017, Tehran, Iran, September 12-14, 2017, Proceedings
EditorsMohammad Reza Mousavi, Jirí Sgall
PublisherSpringer, Cham
ISBN (Electronic)978-3-319-68953-1
ISBN (Print)978-3-319-68952-4
Publication statusPublished - 9 Dec 2017
Event2nd IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science - Tehran, Iran, Islamic Republic of
Duration: 12 Sept 201714 Sept 2017

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference2nd IFIP WG 1.8 International Conference on Topics in Theoretical Computer Science
Abbreviated titleTTCS 2017
Country/TerritoryIran, Islamic Republic of

Bibliographical note

Funding Information:
This work was supported by the Estonian Ministry of Education and Research institutional research grant IUT33-13.

Publisher Copyright:
© 2017 IFIP International Federation for Information Processing.


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