Mapping spaces in Quasi-categories

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Dugger, Daniel
Spivak, David I.
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Abstract
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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], we give a streamlined proof of the Quillen equivalence between quasi-categories and simplicial categories. Some useful material about relative mapping spaces in quasi-categories is developed along the way.
Keywords
Mathematics - Algebraic Topology, Mathematics - Category Theory, 55U40 (Primary) 18G30 (Secondary), 18B99 (Secondary)
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