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arXiv · 2511.13536

Cofinality via Weighted Colimits

Shai Keidar·Lior Yanovski
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Abstract

We prove a refinement of Quillen's Theorem A, providing necessary and sufficient conditions for a functor to be cofinal with respect to diagrams valued in a fixed $\infty$-category. We deduce this from a general duality phenomenon for weighted colimits, which is of independent interest. As a sample application, due to Betts and Dan-Cohen, we describe a simplified formula for the free $\mathbb{E}_\infty$-algebra on an $\mathbb{E}_0$-algebra in a stable rational $\infty$-category .

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Shai Keidar, Lior Yanovski. 2025-11-17. Cofinality via Weighted Colimits. https://arxiv.org/abs/2511.13536

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