Introducing the model structure on sSet-categories:
On the homotopy theory of homotopy theories (the (infinity,1)-category of (infinity,1)-categories):
On comparison of model categories of (∞,1)-categories:
Julie Bergner, A survey of -categories, In: John Baez, Peter May (eds.), Towards Higher Categories The IMA Volumes in Mathematics and its Applications, vol 152, Springer 2007 (arXiv:math/0610239, doi:10.1007/978-1-4419-1524-5_2)
Julia Bergner, Equivalence of models for equivariant -categories, Glasgow Mathematical Journal, Volume 59, Issue 1 (2016) (arXiv:1408.0038, doi:10.1017/S0017089516000136)
On model category presentations of dagger category-objects in by involutive complete Segal spaces (cf. the erratum):
Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy and Applications 10 2 (2008) 149-174 [doi:10.4310/HHA.2008.v10.n2.a8, arXiv:0610291]
Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy and Applications 10 2 (2008) 175-193 [doi:10.4310/HHA.2008.v10.n2.a9, arXiv:0710.2254]
Erratum to “Adding inverses to diagrams encoding algebraic structures” and “Adding inverses to diagrams II: Invertible homotopy theories are spaces”, Homology, Homotopy and Applications 14 1 (2012) 287-291 [doi:10.4310/HHA.2012.v14.n1.a15, arXiv:0710.2254 pp 18]
On the cyclic category and cyclic Segal spaces:
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