A Cellular Nerve for Higher Categories

By C. Berger. 2002

145 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/869d42fe3bb5d728a51999e3477b7ef030b47da5

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Citations in the corpus

Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory (2015, background): “Here is a picture of a certain map 5 → 4 in ∆ and of the corresponding map [5]← [4] in ∆act.”
Polynomial Functors and Trees (2008, background): “In the viewpoint of Berger and Weber, the starting point is the freecategory monad on Grph = PrSh (0 ⇉ 1), the category of directed (non-reflexive) graphs.”
Théories homotopiques dans les topos (2002, background): “Cela contribute aussi l’&etude des structures alg&ebriques d’ordre sup&erieur, comme les !-cat&egories [ 1 ] et les champs de Segal [8].”
Homotopy Theory of Higher Categories: THE MODEL STRUCTURE (2010, background): “See also Bergner [34], Dwyer, Kan and Smith [92], Berger [30], Duskin [86], and others.”
Higher quasi-categories vs higher Rezk spaces (2012, methodology): “This was proved independently by Makkai and Zawadowski in [34] and by Berger in [9].”
Monads with arities and their associated theories (2011, background): “More generally, if E is the category of globular sets, A the full subcategory of globular pasting diagrams, and T the free ω-category monad, the associated theory is Joyal’s cell category [16], and the nerve theorem identifies small ω-categories with cellular sets fulfilling generalised Grothendieck”
Familial 2-functors and parametric right adjoints (2007, unknown): “In [8] theorem(1.17) nerves of algebras of ω-operads are characterised .”
On the Unicity of the Homotopy Theory of Higher Categories (2011, background): “∈Segal∆×n.ON THE UNICITY OF THE HOMOTOPY THEORY OF HIGHER CATEGORIES 25 11. Rezk’s completeSegalΘn-spaces form ahomotopytheory of (∞,n)-categories Here we consider Joyal’s full subcategory Θn of Catn [23, 6, 7]; write i: Θn →Υn for the inclusion functor. Rezk [33, 11.4] identiﬁes the set of morphism”
A cartesian presentation of weak n–categories (2009, background): “The category ‚n has also been studied by Berger [3; 4], with particular application to the theory of iterated loop spaces.”
A Survey of Definitions of n-Category (2001, background): “) More on this duality and on the relationship between definitions J and B is in [61] Clemens Berger, A cellular nerve for higher categories, Université de Nice—Sophia Antipolis Prépublication 602 (2000), 50 pages; also available via http://math.”
The Eckmann–Hilton argument and higher operads (2002, background): “ved in [5] that the n-cells of D(Tr) can be identiﬁed with the morphisms of another category introduced by A.Joyal in [25]. This category was called Ωn and some properties of it were studied later in [8, 11]. More precisely, it was found that the collection of categories Ωn forms an ω-category in Ca”