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 lambda-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2015-03-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/928/pdf |
| _version_ | 1827322879483576320 |
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| author | Thosten Altenkirch James Chapman Tarmo Uustalu |
| author_facet | Thosten Altenkirch James Chapman Tarmo Uustalu |
| author_sort | Thosten Altenkirch |
| collection | DOAJ |
| 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 lambda-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 | 2024-04-25T01:35:50Z |
| format | Article |
| id | doaj.art-a3688075add04e95ab4cc3c872a5867c |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:50Z |
| publishDate | 2015-03-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-a3688075add04e95ab4cc3c872a5867c2024-03-08T09:38:50ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742015-03-01Volume 11, Issue 110.2168/LMCS-11(1:3)2015928Monads need not be endofunctorsThosten AltenkirchJames Chapmanhttps://orcid.org/0000-0001-9036-8252Tarmo Uustaluhttps://orcid.org/0000-0002-1297-0579We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-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.https://lmcs.episciences.org/928/pdfcomputer science - programming languagescomputer science - logic in computer sciencemathematics - category theory |
| spellingShingle | Thosten Altenkirch James Chapman Tarmo Uustalu Monads need not be endofunctors Logical Methods in Computer Science computer science - programming languages computer science - logic in computer science mathematics - category theory |
| 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 | computer science - programming languages computer science - logic in computer science mathematics - category theory |
| url | https://lmcs.episciences.org/928/pdf |
| work_keys_str_mv | AT thostenaltenkirch monadsneednotbeendofunctors AT jameschapman monadsneednotbeendofunctors AT tarmouustalu monadsneednotbeendofunctors |