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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 language | English |
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Title of host publication | 30th EACSL Annual Conference on Computer Science Logic (CSL 2022) |
Editors | Florin Manea, Alex Simpson |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Chapter | 15 |
Number of pages | 17 |
ISBN (Print) | 978-3-95977-218-1 |
DOIs | |
Publication status | Published - 27 Jan 2022 |
Event | 30th EACSL Annual Conference on Computer Science Logic - Virtual Conference Duration: 14 Feb 2022 → 19 Feb 2022 Conference number: 30 http://csl2022.uni-goettingen.de/ |
Publication series
Name | 30th EACSL Annual Conference on Computer Science Logic |
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Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
ISSN (Print) | 1868-8969 |
Conference
Conference | 30th EACSL Annual Conference on Computer Science Logic |
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Abbreviated title | CSL 2022 |
Period | 14/02/22 → 19/02/22 |
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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