AN ALGEBRAIC DEFINITION OF (∞, N)-CATEGORIES

被引：0

作者：

Kachour, Camell ^{[1
]}

机构：

[1] Macquarie Univ, Dept Math, N Ryde, NSW 2109, Australia

来源：

THEORY AND APPLICATIONS OF CATEGORIES | 2015年 / 30卷

关键词：

(infinity; n)-categories; weak infinity-groupoids; homotopy types; WEAK N-CATEGORIES; HOMOTOPY-THEORY; MODELS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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

引用

页码：775 / 807

页数：33

共 38 条

[1]

[Anonymous], 1983, Pursuing Stacks

[2] HIGHER QUASI-CATEGORIES VS HIGHER REZK SPACES [J].

Ara, Dimitri .

JOURNAL OF K-THEORY, 2014, 14 (03) :701-749

[3] THE BROWN-GOLASINSKI MODEL STRUCTURE ON STRICT ∞-GROUPOIDS REVISITED [J].

Ara, Dimitri ;

Metayer, Francois .

HOMOLOGY HOMOTOPY AND APPLICATIONS, 2011, 13 (01) :121-142

[4] n-RELATIVE CATEGORIES: A MODEL FOR THE HOMOTOPY THEORY OF n-FOLD HOMOTOPY THEORIES [J].

Barwick, C. ;

Kan, D. M. .

HOMOLOGY HOMOTOPY AND APPLICATIONS, 2013, 15 (02) :281-300

[5]

Barwick C, 2011, UNICITY HOMOTOPY THE UNICITY HOMOTOPY THE

[6]

Barwick Clark, HOMOLOGY HO IN PRESS

[7]

Barwick Clark, 2012, UNICITY HOMOTOPY HIG

[8] Monoidal globular categories as a natural environment for the theory of weak n-categories [J].

Batanin, MA .

ADVANCES IN MATHEMATICS, 1998, 136 (01) :39-103

[9] On the Penon method of weakening algebraic structures [J].

Batanin, MA .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2002, 172 (01) :1-23

[10] Sheafifiable homotopy model categories [J].

Beke, T .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2000, 129 :447-475

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