<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Lax comma categories of ordered sets |
Publication Date: | 2022-12-27 |
Authors: |
- Maria Manuel Clementino
- Fernando Lucatelli Nunes |
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, when \( X \) is complete, the forgetful functor \( \mathsf{Ord}//X\to\mathsf{Ord} \) is topological. Moreover, \( \mathsf{Ord}//X \) 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 \( \mathsf{Ord}//X \). |
Institution: | DMUC 22-49 |
Online version: | http://www.mat.uc.pt...prints/eng_2022.html |
Download: | Not available |