Lax orthogonal factorisations in monad-quantale-enriched categories
We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$ laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of $(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose corresponding weak factorisation system has em...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2017-09-01
|
| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/2667/pdf |
| _version_ | 1797268624961961984 |
|---|---|
| author | Maria Manuel Clementino Ignacio Lopez Franco |
| author_facet | Maria Manuel Clementino Ignacio Lopez Franco |
| author_sort | Maria Manuel Clementino |
| collection | DOAJ |
| description | We show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$
laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of
$(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal
factorisation system (lofs) whose corresponding weak factorisation system has
embeddings as left part. In addition, we present presheaf submonads and study
the LOFSs they define. This provides a method of constructing weak
factorisation systems on some well-known examples of topological categories
over $\mathsf{Set}$. |
| first_indexed | 2024-04-25T01:35:27Z |
| format | Article |
| id | doaj.art-549b1f85de0e40748ef79be614986dcd |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:27Z |
| publishDate | 2017-09-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-549b1f85de0e40748ef79be614986dcd2024-03-08T09:51:11ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742017-09-01Volume 13, Issue 310.23638/LMCS-13(3:32)20172667Lax orthogonal factorisations in monad-quantale-enriched categoriesMaria Manuel ClementinoIgnacio Lopez FrancoWe show that, for a quantale $V$ and a $\mathsf{Set}$-monad $\mathbb{T}$ laxly extended to $V$-$\mathsf{Rel}$, the presheaf monad on the category of $(\mathbb{T},V)$-categories is simple, giving rise to a lax orthogonal factorisation system (lofs) whose corresponding weak factorisation system has embeddings as left part. In addition, we present presheaf submonads and study the LOFSs they define. This provides a method of constructing weak factorisation systems on some well-known examples of topological categories over $\mathsf{Set}$.https://lmcs.episciences.org/2667/pdfmathematics - category theory |
| spellingShingle | Maria Manuel Clementino Ignacio Lopez Franco Lax orthogonal factorisations in monad-quantale-enriched categories Logical Methods in Computer Science mathematics - category theory |
| title | Lax orthogonal factorisations in monad-quantale-enriched categories |
| title_full | Lax orthogonal factorisations in monad-quantale-enriched categories |
| title_fullStr | Lax orthogonal factorisations in monad-quantale-enriched categories |
| title_full_unstemmed | Lax orthogonal factorisations in monad-quantale-enriched categories |
| title_short | Lax orthogonal factorisations in monad-quantale-enriched categories |
| title_sort | lax orthogonal factorisations in monad quantale enriched categories |
| topic | mathematics - category theory |
| url | https://lmcs.episciences.org/2667/pdf |
| work_keys_str_mv | AT mariamanuelclementino laxorthogonalfactorisationsinmonadquantaleenrichedcategories AT ignaciolopezfranco laxorthogonalfactorisationsinmonadquantaleenrichedcategories |