Monads need not be endofunctors
We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions ca...
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| Format: | Article |
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International federation of Computer Logic
2015
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| Online Access: | https://eprints.nottingham.ac.uk/30436/ |
| _version_ | 1848793984648871936 |
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| author | Altenkirch, Thorsten Chapman, James Uustalu, Tarmo |
| author_facet | Altenkirch, Thorsten Chapman, James Uustalu, Tarmo |
| author_sort | Altenkirch, Thorsten |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between relative monads and monads. Arrows are also an instance of relative monads. |
| first_indexed | 2025-11-14T19:08:59Z |
| format | Article |
| id | nottingham-30436 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:08:59Z |
| publishDate | 2015 |
| publisher | International federation of Computer Logic |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-304362020-05-04T17:04:57Z https://eprints.nottingham.ac.uk/30436/ Monads need not be endofunctors Altenkirch, Thorsten Chapman, James Uustalu, Tarmo We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between relative monads and monads. Arrows are also an instance of relative monads. International federation of Computer Logic 2015-03-06 Article PeerReviewed Altenkirch, Thorsten, Chapman, James and Uustalu, Tarmo (2015) Monads need not be endofunctors. Logical Methods in Computer Science, 11 (1:3). pp. 1-40. ISSN 1860-5974 monads adjunctions monoids skew-monoidal categories functional programming http://www.www.lmcs-online.org/ojs/viewarticle.php?id=946&layout=abstract doi:10.2168/LMCS-11(1:3)2015 doi:10.2168/LMCS-11(1:3)2015 |
| spellingShingle | monads adjunctions monoids skew-monoidal categories functional programming Altenkirch, Thorsten Chapman, James Uustalu, Tarmo Monads need not be endofunctors |
| title | Monads need not be endofunctors |
| title_full | Monads need not be endofunctors |
| title_fullStr | Monads need not be endofunctors |
| title_full_unstemmed | Monads need not be endofunctors |
| title_short | Monads need not be endofunctors |
| title_sort | monads need not be endofunctors |
| topic | monads adjunctions monoids skew-monoidal categories functional programming |
| url | https://eprints.nottingham.ac.uk/30436/ https://eprints.nottingham.ac.uk/30436/ https://eprints.nottingham.ac.uk/30436/ |