Mapping spaces in Quasi-categories
Daniel Dugger, David I. Spivak
TL;DR
This paper explores the relationship between quasi-categories and simplicial categories by applying homotopy theory and rigidification techniques, providing a streamlined proof of their Quillen equivalence.
Contribution
It introduces a simplified proof of the Quillen equivalence between quasi-categories and simplicial categories using homotopy function complexes and rigidification methods.
Findings
Established a Quillen equivalence between quasi-categories and simplicial categories
Developed new insights into relative mapping spaces in quasi-categories
Provided streamlined proofs leveraging Dwyer-Kan theory
Abstract
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.
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