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

Abstract

In this paper we complete a chain of explicit Quillen equivalences between the model category for ${\Theta }_{n+1}$-spaces and the model category of small categories enriched in ${\Theta }_n$-spaces. The Quillen equivalences given here connect Segal category objects in ${\Theta }_n$-spaces, complete Segal objects in ${\Theta }_n$-spaces, and ${\Theta }_{n+1}$-spaces.

28 pages; minor expository changes from previous version

References in corpus (3)

• (Op)lax natural transformations, twisted quantum field theories, and "even higher" Morita categories
• Rectification of enriched infinity-categories
• On the equivalence between ${\Theta }_n$-spaces and iterated Segal spaces

Cited by in corpus (7)

• A homotopy coherent cellular nerve for bicategories
• Univalence and completeness of Segal objects
• Quasi-Categories vs. Segal Spaces: Cartesian Edition
• Segalification and the Boardman-Vogt tensor product
• Higher categories of push-pull spans, I: Construction and applications
• Discreteness and completeness for ${\Theta }_n$-models of $(\infty ,n)$-categories
• A pasting theorem for iterated Segal spaces