Theorem A for marked 2-categories

Fernando Abellán García; Walker H. Stern

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arXiv · 2002.12817

Theorem A for marked 2-categories

Fernando Abellán García·Walker H. Stern

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Abstract

In this work, we prove a generalization of Quillen's Theorem A to 2-categories equipped with a special set of morphisms which we think of as weak equivalences, providing sufficient conditions for a 2-functor to induce an equivalence on $(\infty,1)$-localizations. When restricted to 1-categories with all morphisms marked, our theorem retrieves the classical Theorem A of Quillen. We additionally state and provide evidence for a new conjecture: the cofinality conjecture, which describes the relation between a conjectural theory of marked $(\infty,2)$-colimits and our generalization of Theorem A.

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Fernando Abellán García, Walker H. Stern. 2020-02-28. Theorem A for marked 2-categories. https://arxiv.org/abs/2002.12817

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