# Homotopy theory of higher categories

Abstract : This is the first draft of a book about higher categories approached by iterating Segal's method, as in Tamsamani's definition of $n$-nerve and Pelissier's thesis. If $M$ is a tractable left proper cartesian model category, we construct a tractable left proper cartesian model structure on the category of $M$-precategories. The procedure can then be iterated, leading to model categories of $(\infty , n)$-categories.
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Cited literature [206 references]

https://hal.archives-ouvertes.fr/hal-00449826
Contributor : Carlos Simpson <>
Submitted on : Friday, January 22, 2010 - 5:26:02 PM
Last modification on : Tuesday, December 8, 2020 - 9:47:59 AM
Long-term archiving on: : Friday, June 18, 2010 - 1:19:38 AM

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### Identifiers

• HAL Id : hal-00449826, version 1
• ARXIV : 1001.4071

### Citation

Carlos Simpson. Homotopy theory of higher categories. Cambridge University Press, 19, 2011, New mathematical monographs, 9780521516952. ⟨hal-00449826⟩

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