New York Journal of Mathematics
Volume 27 (2021), 508-550


Aaron Mazel-Gee

Model ∞-categories II: Quillen adjunctions

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Published: April 12, 2021.
Keywords: ∞-category, model structure, adjunction, Quillen adjunction, enriched, two-variable, monoidal, symmetric monoidal.
Subject: 55U35, 18A40, 18G55, 55P60, 55U40.

We prove that various structures on model ∞-categories descend to corresponding structures on their localizations: (i) Quillen adjunctions; (ii) two-variable Quillen adjunctions; (iii) monoidal and symmetric monoidal model structures; and (iv) enriched model structures.


We would like to thank Geoffroy Horel, Zhen Lin Low, and Adeel Khan Yusufzai for their helpful comments; Dmitri Pavlov, for spotting and helping us correct a small mistake in a previous version; and the NSF graduate research fellowship program (grant DGE-1106400) for financial support during the time that this work was carried out.

Author information

Aaron Mazel-Gee:
Division of Physics, Mathematics and Astronomy
California Institute of Technology
1200 E California Blvd
Pasadena, CA 91125, USA