Abstract / Description of output
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e., the property for an effect to commute with all other effects, may be formulated for strong monads acting on symmetric monoidal categories. We identify three equivalent conditions which characterise the existence of the centre of a strong monad (some of which relate it to the premonoidal centre of Power and Robinson) and we show that every strong monad on many well-known naturally occurring categories does admit a centre, thereby showing that this new notion is ubiquitous. More generally, we study central submonads, which are necessarily commutative, just like the centre of a strong monad. We provide a computational interpretation by formulating equational theories of lambda calculi equipped with central submonads, we describe categorical models for these theories and prove soundness, completeness and internal language results for our semantics.
Original language | English |
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Title of host publication | 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science |
Place of Publication | Boston, Massachusetts |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 1-13 |
Number of pages | 13 |
ISBN (Electronic) | 9798350335873 |
ISBN (Print) | 9798350335880 |
DOIs | |
Publication status | Published - 14 Jul 2023 |
Event | The 38th Annual ACM/IEEE Symposium on Logic in Computer Science - Boston University, Boston, United States Duration: 26 Jun 2023 → 29 Jun 2023 https://lics.siglog.org/lics23/ |
Publication series
Name | Proceedings of the ACM/IEEE Symposium on Logic in Computer Science |
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Publisher | IEEE |
ISSN (Print) | 1043-6871 |
ISSN (Electronic) | 2575-5528 |
Symposium
Symposium | The 38th Annual ACM/IEEE Symposium on Logic in Computer Science |
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Abbreviated title | LICS 2023 |
Country/Territory | United States |
City | Boston |
Period | 26/06/23 → 29/06/23 |
Internet address |
Keywords / Materials (for Non-textual outputs)
- computer science
- computer languages
- computational modeling
- semantics
- mathematical models