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Kleisli categories, T-categories and internal categories
Theory and applications of categories, Tome 41 (2024), pp. 1108-1159 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We investigate the properties of the Kleisli category Kl T of a monad T on a category E and in particular the existence of (some kind of) pullbacks. This culminates when the monad is cartesian. In this case, we show that any T-category in E in the sense of A. Burroni coincides with a special kind of internal category in Kl T. Thus, it is the case in particular for T-operads and T-multicategories. More unexpectedly, this, in turn, sheds new conceptual lights on internal categories and n-categories.

Publié le :
Classification : 18C20, 18D40, 18M60, 18M65, 18N50
Keywords: Internal categories and groupoids, Kleisli categories, T-categories, internal n-categories and n-groupoids, operads, multicategories. 
@article{TAC_2024_41_a33,
     author = {Dominique Bourn},
     title = {Kleisli categories, {T-categories} and internal categories},
     journal = {Theory and applications of categories},
     pages = {1108--1159},
     year = {2024},
     volume = {41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a33/}
}
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Dominique Bourn. Kleisli categories, T-categories and internal categories. Theory and applications of categories, Tome 41 (2024), pp. 1108-1159. http://geodesic.mathdoc.fr/item/TAC_2024_41_a33/