Geodesic
KZ-pseudomonads and Kan injectivity
Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 430-478 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We introduce the notion of Kan injectivity in 2-categories and study its properties. For an adequate 2-category K, we show that every set of morphisms H induces a KZ-pseudomonad on K whose 2-category of pseudoalgebras is the locally full sub-2-category of all objects (left) Kan injective with respect to H and morphisms preserving Kan extensions. The main ingredient is the construction of a (pseudo)chain whose appropriate "convergence" is ensured by a small object argument.

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Classification : 18D70, 18D65, 18N10, 18N15
Keywords: 2-category, Kan injectivity, KZ-pseudomonad, small object argument 
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     author = {Ivan Di Liberti and Gabriele Lobbia and Lurdes Sousa},
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Ivan Di Liberti; Gabriele Lobbia; Lurdes Sousa. KZ-pseudomonads and Kan injectivity. Theory and applications of categories, Bunge Festschrift, Tome 40 (2024), pp. 430-478. http://geodesic.mathdoc.fr/item/TAC_2024_40_a15/