Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A characterization of fibrant Segal categories

Author(s): Julia E. Bergner
Journal: Proc. Amer. Math. Soc. 135 (2007), 4031-4037.
MSC (2000): Primary 55U35; Secondary 18G30
Posted: August 29, 2007
MathSciNet review: 2341955
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Abstract: In this note we prove that Reedy fibrant Segal categories are fibrant objects in the model category structure $\mathcal{SeCat}_c$ . Combining this result with a previous one, we thus have that the fibrant objects are precisely the Reedy fibrant Segal categories. We also show that the analogous result holds for Segal categories that are fibrant in the projective model structure on simplicial spaces, considered as objects in the model structure $\mathcal{SeCat}_f$ .

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