The goal of this article is to emphasize the role of cubical sets in enriched category theory and infinity-category theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many infinity-categories appearing in the context of homological algebra.
Keywords: Enriched categories, cubical sets
2020 MSC: 18D20,18N50
Theory and Applications of Categories, Vol. 35, 2020, No. 18, pp 622-664.