Categorical Theory of $(\infty,\omega)$-Categories

TL;DR

This paper develops the theory of $( abla, ext{omega})$-categories, generalizing key category theory results like the Yoneda lemma and Kan extensions to this higher categorical context.

Contribution

It introduces a comprehensive framework for $( abla, ext{omega})$-categories, extending classical results to this new setting.

Findings

Generalized the lax Grothendieck construction for $( abla, ext{omega})$-categories

Extended the Yoneda lemma to higher categorical structures

Developed notions of lax (co)limits and Kan extensions in this context

Abstract

This text is dedicated to the development of the theory of $(\infty,\omega)$-categories. We present generalizations of standard results from category theory, such as the lax Grothendieck construction, the Yoneda lemma, lax (co)limits and lax Kan extensions, among others.