Aspects of algebraic Algebras
In this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg-Moore category, for a Kock-Z\"oberlein monad on an order-enriched category. Firstly, we give a characterisation of free algebras in the spirit of domain theory. Secondly, we study the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2017-07-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/2644/pdf |
| _version_ | 1797268611906142208 |
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| author | Dirk Hofmann Lurdes Sousa |
| author_facet | Dirk Hofmann Lurdes Sousa |
| author_sort | Dirk Hofmann |
| collection | DOAJ |
| description | In this paper we investigate important categories lying strictly between the
Kleisli category and the Eilenberg-Moore category, for a Kock-Z\"oberlein monad
on an order-enriched category. Firstly, we give a characterisation of free
algebras in the spirit of domain theory. Secondly, we study the existence of
weighted (co)limits, both on the abstract level and for specific categories of
domain theory like the category of algebraic lattices. Finally, we apply these
results to give a description of the idempotent split completion of the Kleisli
category of the filter monad on the category of topological spaces. |
| first_indexed | 2024-04-25T01:35:14Z |
| format | Article |
| id | doaj.art-266296fb8151419588a1263532bffa54 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:14Z |
| publishDate | 2017-07-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-266296fb8151419588a1263532bffa542024-03-08T09:51:11ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742017-07-01Volume 13, Issue 310.23638/LMCS-13(3:4)20172644Aspects of algebraic AlgebrasDirk HofmannLurdes SousaIn this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg-Moore category, for a Kock-Z\"oberlein monad on an order-enriched category. Firstly, we give a characterisation of free algebras in the spirit of domain theory. Secondly, we study the existence of weighted (co)limits, both on the abstract level and for specific categories of domain theory like the category of algebraic lattices. Finally, we apply these results to give a description of the idempotent split completion of the Kleisli category of the filter monad on the category of topological spaces.https://lmcs.episciences.org/2644/pdfmathematics - category theory06b23, 06b35, 18a35, 18a40, 18b30, 18c20, 18d20 |
| spellingShingle | Dirk Hofmann Lurdes Sousa Aspects of algebraic Algebras Logical Methods in Computer Science mathematics - category theory 06b23, 06b35, 18a35, 18a40, 18b30, 18c20, 18d20 |
| title | Aspects of algebraic Algebras |
| title_full | Aspects of algebraic Algebras |
| title_fullStr | Aspects of algebraic Algebras |
| title_full_unstemmed | Aspects of algebraic Algebras |
| title_short | Aspects of algebraic Algebras |
| title_sort | aspects of algebraic algebras |
| topic | mathematics - category theory 06b23, 06b35, 18a35, 18a40, 18b30, 18c20, 18d20 |
| url | https://lmcs.episciences.org/2644/pdf |
| work_keys_str_mv | AT dirkhofmann aspectsofalgebraicalgebras AT lurdessousa aspectsofalgebraicalgebras |