Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations

Jaco Ruit

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arXiv · 2408.15190

Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations

Jaco Ruit

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Abstract

We study the framework of $\infty$-equipments which is designed to produce well-behaved theories for different generalizations of $\infty$-categories in a synthetic and uniform fashion. We consider notions of (lax) functors between these equipments, closed monoidal structures on these equipments, and fibrations internal to these equipments. As a main application, we will demonstrate that the foundations of internal $\infty$-category theory can be readily obtained using this formalism.

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BibTeX RIS

Jaco Ruit. 2024-08-27. Formal category theory in $\infty$-equipments II: Lax functors, monoidality and fibrations. https://arxiv.org/abs/2408.15190

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