Homotopy theory of higher categories

Carlos Simpson (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Catégories et ensembles [math.CT]; Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]

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