Geodesic
An algebraic definition of ($\infty$,n)-categories
Theory and applications of categories, Tome 30 (2015), pp. 751-774

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In this paper we define a sequence of monads $T^{(\infty,n)} (n\in\mathbb{N})$ on the category $\infty-Gr$ of $\infty$-graphs. We conjecture that algebras for $\T^{(\infty,0)}$, which are defined in a purely algebraic setting, are models of $\infty$-groupoids. More generally, we conjecture that $T^{(\infty,n)}$-algebras are models for $(\infty,n)$-categories. We prove that our $(\infty,0)$-categories are bigroupoids when truncated at level 2.

Publié le :
Classification : 18B40, 18C15, 18C20, 18G55, 20L99, 55U35, 55P15
Keywords: ($\infty$, n)-categories, weak $\infty$-groupoids, homotopy types 
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     author = {Camell Kachour},
     title = {An algebraic definition of ($\infty$,n)-categories},
     journal = {Theory and applications of categories},
     pages = {751--774},
     publisher = {mathdoc},
     volume = {30},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a21/}
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Camell Kachour. An algebraic definition of ($\infty$,n)-categories. Theory and applications of categories, Tome 30 (2015), pp. 751-774. http://geodesic.mathdoc.fr/item/TAC_2015_30_a21/