On cofinal functors of $\infty$-bicategories

Fernando Abellán; Walker H. Stern

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arXiv · 2304.07028

On cofinal functors of $\infty$-bicategories

Fernando Abellán·Walker H. Stern

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Abstract

In this work, we study the notion of cofinal functor of $\infty$-bicategories with respect to the theory of partially lax colimits. The main result of this paper is a characterization of cofinal functors of $\infty$-bicategories via generalizations of the conditions of Quillen's Theorem A. As a key ingredient for the proof of our main theorem we produce for every functor of $\infty$-bicategories $f:\mathbb{C} \to \mathbb{D}$ an outer 2-Cartesian fibration $\mathbb{F}(\mathbb{C})\to \mathbb{D}$ which we identify it as the free fibration on the functor $f$.

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BibTeX RIS

Fernando Abellán, Walker H. Stern. 2023-04-14. On cofinal functors of $\infty$-bicategories. https://arxiv.org/abs/2304.07028

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