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arXiv · 2405.12118

Group completion via the action $\infty$-category

Georg Lehner
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Abstract

We give a generalization of Quillen's $S^{-1}S$ construction for arbitrary $E_n$-monoids as an $E_{n-1}$-monoidal $\infty$-category and show that its realization models the group completion provided that $n \geq 2$. We will also show how this construction is related to a variety of other constructions of the group completion.

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Georg Lehner. 2024-05-20. Group completion via the action $\infty$-category. https://arxiv.org/abs/2405.12118

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