Comparison of models for $(\infty ,n)$-categories, I

Abstract

While many different models for $(\infty ,1)$-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 $(\infty ,n)$-categories. In this paper, we establish model structures for some naturally arising categories of objects which should be thought of as $(\infty ,n)$-categories. Furthermore, we establish Quillen equivalences between them.

27 pages; updated references

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