Geodesic
On the duality between trees and disks
Theory and applications of categories, Tome 24 (2010), pp. 418-450 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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A combinatorial category Disk was introduced by André Joyal to play a role in his definition of weak $\omega$-category. He defined the category $\Theta$ to be dual to Disk. In the ensuing literature, a more concrete description of $\Theta$ was provided. In this paper we provide another proof of the dual equivalence and introduce various categories equivalent to Disk or $\Theta$, each providing a helpful viewpoint.

Classification : 18D05, 18D20, 18D35
Keywords: delta, disk, duality, globular set, omega-category, theta-category, tree 
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     author = {David Oury},
     title = {On the duality between trees and disks},
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     pages = {418--450},
     year = {2010},
     volume = {24},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_24_a15/}
}
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David Oury. On the duality between trees and disks. Theory and applications of categories, Tome 24 (2010), pp. 418-450. http://geodesic.mathdoc.fr/item/TAC_2010_24_a15/