<Reference List> | |
Type: | Preprint |
National /International: | International |
Title: | Lax comma categories: cartesian closedness, extensivity, topologicity, and descent |
Publication Date: | 2024-05-08 |
Authors: |
- Maria Manuel Clementino
- Fernando Lucatelli Nunes - Rui Rodrigues de Abreu Fernandes Prezado |
Abstract: | We investigate the properties of lax comma categories over a base category \( X \), focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from \( \mathsf{Cat} //X \) to \( \mathsf{Cat} \) is topological if and only if \( X \) is large-complete. Moreover, we provide conditions for \( \mathsf{Cat} // X \) to be complete, cocomplete, extensive and cartesian closed. We analyze descent in \( \mathsf{Cat} // X \) and identify necessary conditions for effective descent morphisms. Our findings contribute to the literature on lax comma categories and provide a foundation for further research in 2-dimensional Janelidze's Galois theory. |
Institution: | DMUC 24-26 |
Online version: | http://www.mat.uc.pt...prints/eng_2024.html |
Download: | Not available |