LAX COMMA CATEGORIES: CARTESIAN CLOSEDNESS, EXTENSIVITY, TOPOLOGICITY, AND DESCENT
Publication date
2024
Authors
Clementino, Maria Manuel
Nunes, Fernando Lucatelli
Prezado, Rui
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Supervisors
DOI
Document Type
Article
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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.
Keywords
2-dimensional category theory, cartesian closed category, effective descent morphism, exponentiability, Galois theory, Grothendieck descent theory, lax comma categories, topological functor, Taverne, Mathematics (miscellaneous)
Citation
Clementino, M M, Nunes, F L & Prezado, R 2024, 'LAX COMMA CATEGORIES : CARTESIAN CLOSEDNESS, EXTENSIVITY, TOPOLOGICITY, AND DESCENT', Theory and Applications of Categories, vol. 41, pp. 516-530.