The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Introduction
1. Cubical sets and marked cubical sets
2. Model structure on marked cubical sets
3. Model structure on structurally marked cubical sets
4. Joyal model structure on cubical sets
5. Cones in cubical sets
6. Comparison with the Joyal model structure
7. Mapping spaces in cubical quasicategories
A. Verification of identities on $\theta $
Brandon Doherty, University of Western Ontario, London, Ontario, Canada, Krzysztof Kapulkin, University of Western Ontario, London, Ontario, Canada.
