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arXiv · 2605.03150

Free algebras via monoidal envelopes

Max Blans·Sil Linskens
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Abstract

For any morphism of $\infty$-operads $\mathcal{P} \to \mathcal{O}$, we show that the free $\mathcal{O}$-algebra on a $\mathcal{P}$-algebra admits an explicit formula as the colimit over the $\mathcal{O}$-monoidal envelope of $\mathcal{P}$, providing a new and simple proof of the existence of relative free $\mathcal{O}$-algebras.

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Max Blans, Sil Linskens. 2026-05-04. Free algebras via monoidal envelopes. https://arxiv.org/abs/2605.03150

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