Year: 2026
Type: article
Abstract: We show that a variant of Lurie’s \infty -operads, where the category of finite pointed sets is replaced by that of spans of finite sets, can be identified as precisely the Lawvere theories of the analytic monads previously studied by Gepner, Kock, and the author. This gives an equivalence between \infty -operads (or more precisely a “flagged” or “pinned” version thereof) and analytic monads, with an \infty -operad \mathcal{O} corresponding to the monad for \mathcal{O} -algebras in spaces. In particular, the \infty -operad \mathcal{O} is completely determined by this monad. To prove this we extend the equivalence between \infty -categorical Lawvere theories and algebraic monads, due to Gepner, Groth, and Nikolaus, to the many-object (or many-sorted) case.
Source: Documenta Mathematica
DOI: 10.4171/dm/1092
Author: Rune Haugseng
Institution: Norwegian University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4313533159