Geodesic
The comprehensive factorization of Burroni's T-functors
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 206-249.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal) T-categories and their functors. This context provides for some expected applications and some unexpected connections. For example, it lets us deduce that the comprehensive factorization is also available for functors of Lambek's multicategories. In topology, it leads to the insight that the role of discrete cofibrations is played by perfect maps, with the comprehensive factorization of a continuous map of Tychonoff spaces given by its fibrewise compactification.
Publié le :
Classification : 18A32, 18A30, 18C15, 18D30, 54C10
Keywords: T-graph, T-category, T-functor, discrete cofibration, comprehensive factorization, multicategory, perfect map, wide pullback, small-topological functor 
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Walter Tholen; Leila Yeganeh. The comprehensive factorization of Burroni's T-functors. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 206-249. http://geodesic.mathdoc.fr/item/TAC_2021_36_a7/