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 Cat//X to Cat is topological if and only if X is large-complete. Moreover, we provide conditions for Cat//X to be complete, cocomplete, extensive and cartesian closed. We analyze descent in 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.
| Original language | English |
|---|---|
| Pages (from-to) | 516-530 |
| Number of pages | 15 |
| Journal | Theory and Applications of Categories |
| Volume | 41 |
| Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:© Maria Manuel Clementino, Fernando Lucatelli Nunes and Rui Prezado, 2024.
Keywords
- 2-dimensional category theory
- cartesian closed category
- effective descent morphism
- exponentiability
- Galois theory
- Grothendieck descent theory
- lax comma categories
- topological functor
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