Localisable Monads

Carmen Constantin, Nuiok Dicaire, Chris Heunen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip monads with fine-grained structure in a ''top-down'' way, using techniques from tensor topology. This provides an intrinsic theory of local computational effects without needing to know how constituent effects interact beforehand. Specifically, any monoidal category decomposes as a sheaf of local categories over a base space. We identify a notion of localisable monads which characterises when a monad decomposes as a sheaf of monads. Equivalently, localisable monads are formal monads in an appropriate presheaf 2-category, whose algebras we characterise. Three extended examples demonstrate how localisable monads can interpret the base space as locations in a computer memory, as sites in a network of interacting agents acting concurrently, and as time in stochastic processes.
Original languageEnglish
Title of host publication30th EACSL Annual Conference on Computer Science Logic (CSL 2022)
EditorsFlorin Manea, Alex Simpson
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Chapter15
Number of pages17
ISBN (Print)978-3-95977-218-1
DOIs
Publication statusPublished - 27 Jan 2022
Event30th EACSL Annual Conference on Computer Science Logic - Virtual Conference
Duration: 14 Feb 202219 Feb 2022
Conference number: 30
http://csl2022.uni-goettingen.de/

Publication series

Name30th EACSL Annual Conference on Computer Science Logic
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
ISSN (Print)1868-8969

Conference

Conference30th EACSL Annual Conference on Computer Science Logic
Abbreviated titleCSL 2022
Period14/02/2219/02/22
Internet address

Keywords / Materials (for Non-textual outputs)

  • Monad
  • monoidal category
  • Presheaf
  • Central idempotent
  • Graded monad
  • Indexed monad
  • Formal monad
  • Strong monad
  • Commutative monad

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