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Lax comma categories: cartesian closedness, extensivity, topologicity, and descent
Theory and applications of categories, Tome 41 (2024), pp. 516-530 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

Publié le :
Classification : 18N10, 18N15, 18A05, 18A22, 18A40
Keywords: lax comma categories, Grothendieck descent theory, Galois theory, 2-dimensional category theory, topological functor, effective descent morphism, cartesian closed category, exponentiability 
@article{TAC_2024_41_a15,
     author = {Maria Manuel Clementino and Fernando Lucatelli Nunes and Rui Prezado},
     title = {Lax comma categories: cartesian closedness, extensivity, topologicity,  and descent},
     journal = {Theory and applications of categories},
     pages = {516--530},
     year = {2024},
     volume = {41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a15/}
}
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Maria Manuel Clementino; Fernando Lucatelli Nunes; Rui Prezado. Lax comma categories: cartesian closedness, extensivity, topologicity,  and descent. Theory and applications of categories, Tome 41 (2024), pp. 516-530. http://geodesic.mathdoc.fr/item/TAC_2024_41_a15/