Segalification and the Boardman–Vogt tensor product

Barkan, Shaul; Steinebrunner, Jan

doi:10.2140/agt.2025.25.5439

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ISSN (electronic): 1472-2739

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Segalification and the Boardman–Vogt tensor product

Shaul Barkan and Jan Steinebrunner

Algebraic & Geometric Topology 25 (2025) 5439–5462

DOI: 10.2140/agt.2025.25.5439

Abstract

We develop an analogue of Dugger and Spivak’s necklace formula, providing an explicit description of the Segal space generated by an arbitrary simplicial space. We apply this to obtain a formula for the Segalification of $n$ -fold simplicial spaces, a new proof of the invariance of right fibrations, and a new construction of the Boardman–Vogt tensor product of $\infty$ -operads, for which we also derive an explicit formula.

Keywords

Segal space, infinity-category, infinity-operad, Boardman–Vogt tensor product

Mathematical Subject Classification

Primary: 18N60, 18N65, 18N70

References

Publication

Received: 5 April 2023

Revised: 22 February 2024

Accepted: 28 October 2024

Published: 18 December 2025

Authors

Shaul Barkan
Hebrew University of Jerusalem Tel Aviv Israel

Jan Steinebrunner
Gonville & Caius College Cambridge University Cambridge United Kingdom

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Volume 25, issue 9 (2025)