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Graded Algebraic Theories
We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of categories, which extends the equivalence for monads. We also give...
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| Formato: | Online Artículo Texto |
| Lenguaje: | English |
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2020
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| Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7788601/ http://dx.doi.org/10.1007/978-3-030-45231-5_21 |
| _version_ | 1783633061270781952 |
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| author | Kura, Satoshi |
| author_facet | Kura, Satoshi |
| author_sort | Kura, Satoshi |
| collection | PubMed |
| description | We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of categories, which extends the equivalence for monads. We also give sums and tensor products of graded algebraic theories to combine computational effects as an example of importing techniques based on algebraic theories to graded monads. |
| format | Online Article Text |
| id | pubmed-7788601 |
| institution | National Center for Biotechnology Information |
| language | English |
| publishDate | 2020 |
| record_format | MEDLINE/PubMed |
| spelling | pubmed-77886012021-01-07 Graded Algebraic Theories Kura, Satoshi Foundations of Software Science and Computation Structures Article We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of categories, which extends the equivalence for monads. We also give sums and tensor products of graded algebraic theories to combine computational effects as an example of importing techniques based on algebraic theories to graded monads. 2020-04-17 /pmc/articles/PMC7788601/ http://dx.doi.org/10.1007/978-3-030-45231-5_21 Text en © The Author(s) 2020 Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. |
| spellingShingle | Article Kura, Satoshi Graded Algebraic Theories |
| title | Graded Algebraic Theories |
| title_full | Graded Algebraic Theories |
| title_fullStr | Graded Algebraic Theories |
| title_full_unstemmed | Graded Algebraic Theories |
| title_short | Graded Algebraic Theories |
| title_sort | graded algebraic theories |
| topic | Article |
| url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7788601/ http://dx.doi.org/10.1007/978-3-030-45231-5_21 |
| work_keys_str_mv | AT kurasatoshi gradedalgebraictheories |