The author presents a theory of two-sided cartesian fibrations within the framework of synthetic (∞, 1)-category theory, focusing on characterizations and closure properties.
The construction of opposites for weak ω-categories facilitates the development of category theory.
Categorical spectra, a higher-categorical analogue of spectra, are equivalent to pointed $(\infty, \mathbb{Z})$-categories, providing a more algebraic understanding of these stable structures.