Lax comma categories: cartesian closedness, extensivity, topologicity, and descent (Preprint)

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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
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