Comparison of models for (∞, n)-categories, I

Julia E. Bergner, Charles Rezk

Research output: Contribution to journalArticlepeer-review


While many different models for (∞, 1)-categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for (1, n)-categories. In this paper, we establish model structures for some naturally arising categories of objects which should be thought of as (∞, n)-categories. Furthermore, we establish Quillen equivalences between them.

Original languageEnglish (US)
Pages (from-to)2163-2202
Number of pages40
JournalGeometry and Topology
Issue number4
StatePublished - Jul 19 2013


  • (∞, n)-categories
  • Enriched categories
  • Θn-spaces

ASJC Scopus subject areas

  • Geometry and Topology


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