Segalification and the Boardman-Vogt tensor product

Abstract

We develop an analog 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.

24 pages, one figure. v2: several minor changes in response to referee report. Also added a more detailed comparison to Lurie's BV tensor product to fix a problem pointed out to us by Manuel Krannich. v3: updated references, to appear in Algebraic & Geometric Topology