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- W4313305105 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} //Xto 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 $mathsf{Ord} //X$." @default.
- W4313305105 created "2023-01-06" @default.
- W4313305105 creator A5029577833 @default.
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- W4313305105 date "2022-12-27" @default.
- W4313305105 modified "2023-09-29" @default.
- W4313305105 title "Lax comma categories of ordered sets" @default.
- W4313305105 doi "https://doi.org/10.48550/arxiv.2212.13541" @default.
- W4313305105 hasPublicationYear "2022" @default.
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