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arXiv · 2102.05192

Quasi-Categories vs. Segal Spaces: Cartesian Edition

Nima Rasekh
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Abstract

We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets, on bisimplicial spaces, on bisimplicial sets, on marked simplicial spaces. The main way to prove these equivalences is by using the Quillen equivalences between quasi-categories and complete Segal spaces as defined by Joyal-Tierney and the straightening construction due to Lurie.

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Nima Rasekh. 2021-02-10. Quasi-Categories vs. Segal Spaces: Cartesian Edition. https://doi.org/10.1007/s40062-021-00288-2

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