nLab Julie Bergner

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Selected writings

Introducing the model structure on sSet-categories:

• Julie Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043-2058 (arXiv:0406507, doi:10.1090/S0002-9947-06-03987-0)

On the homotopy theory of homotopy theories (the (infinity,1)-category of (infinity,1)-categories):

• Julia Bergner, Three models for the homotopy theory of homotopy theories, Topology Volume 46, Issue 4, September 2007, Pages 397-436 (arXiv:math/0504334, doi:10.1016/j.top.2007.03.002)

On comparison of model categories of (∞,1)-categories:

• Julie Bergner, A survey of $(\infty,1)$-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 $(\infty,1)$-categories, Glasgow Mathematical Journal, Volume 59, Issue 1 (2016) (arXiv:1408.0038, doi:10.1017/S0017089516000136)

On model categories presenting $(\infty,0)$-categories, namely models for $\infty$-groupoids (such as the model structure on simplicial groupoids) akin to corresponding models for $(\infty,1)$-categories (such as the model structure on simplicial categories):

• Julia E. Bergner, Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy Appl. 10 2 (2008) 175-193 [doi:10.4310/HHA.2008.v10.n2.a9, doi:0710.2254, erratum:doi:10.4310/HHA.2012.v14.n1.a15]

On the cyclic category and cyclic Segal spaces:

• Julia E. Bergner, Walker H. Stern: Cyclic Segal Spaces [arXiv:2409.11945]

Related entries

• model category

• (∞,1)-category

• simplicially enriched category

• complete Segal space

• (∞,n)-category

• cobordism hypothesis

category: people