2026-08-17T02:40:29Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15735 2024-03-06T10:56:04Z ddc:004 open_access

Localisable Monads Constantin, Carmen Dicaire, Nuiok Heunen, Chris Monad Monoidal category Presheaf Central idempotent Graded monad Indexed monad Formal monad Strong monad Commutative monad Monads govern computational side-effects in programming semantics. A collection of monads can be combined together in a local-to-global way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we start with a single monad and equip it with a fine-grained structure by 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Carmen Constantin and Nuiok Dicaire and Chris Heunen 2022 Is Part Of LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2022.15 urn:nbn:de:0030-drops-157353 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.15 eng https://creativecommons.org/licenses/by/4.0/legalcode