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https://hdl.handle.net/10316/114082
Title: | Lax comma categories of ordered sets | Authors: | Clementino, Maria Manuel Lucatelli Nunes, Fernando |
Keywords: | Effective descent morphisms; laxcomma2-categories; comma categories; ex- ponentiability; cartesian closed categories; topological functors; enriched categories; Ord- enriched categories | Issue Date: | 27-Dec-2022 | Publisher: | Taylor and Francis Ltd. | Project: | programme “Oberwolfach Leibniz Fellows” by the Mathematisches Forschungsinstitut Oberwolfach in 2022 UIDB/00324/2020 |
Serial title, monograph or event: | Quaestiones Mathematicae | Volume: | 46 | Issue: | sup1 | Abstract: | Let $\mathsf{Ord} $ be the category of (pre)ordered sets. Unlike $\mathsf{Ord}/X$, whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category $\mathsf{Ord} //X$. In this paper we show that the forgetful functor $\mathsf{Ord} //X\to \mathsf{Ord} $ is topological if and only if $X$ is complete. Moreover, under suitable hypothesis, $\mathsf{Ord} // X$ is complete and cartesian closed if and only if $X$ is. We end by analysing descent in this category. Namely, when $X$ is complete and cartesian closed, we show that, for a morphism in $\mathsf{Ord} //X$, being pointwise effective for descent in $\mathsf{Ord} $ is sufficient, while being effective for descent in $\mathsf{Ord} $ is necessary, to be effective for descent in $\mathsf{Ord} //X$. | Description: | 12 pages | URI: | https://hdl.handle.net/10316/114082 | ISSN: | 1607-3606 1727-933X |
DOI: | 10.2989/16073606.2023.2247729 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
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