# Rigidification of quasi-categories

@article{Dugger2009RigidificationOQ,
title={Rigidification of quasi-categories},
author={Daniel Dugger and David I. Spivak},
journal={arXiv: Category Theory},
year={2009}
}
• Published 2009
• Mathematics
• arXiv: Category Theory
We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from Lurie's "Higher Topos Theory" regarding the rigidification process.
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We apply the Dwyer-Kan theory of homotopy function complexes in model categories to the study of mapping spaces in quasi-categories. Using this, together with our work on rigidification from [DS1],Expand
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