Segalification and the Boardman-Vogt tensor product

TL;DR

This paper introduces explicit formulas for Segalification of simplicial spaces and the Boardman-Vogt tensor product of ∞-operads, advancing the understanding of these constructions in higher category theory.

Contribution

It provides explicit formulas for Segalification and the Boardman-Vogt tensor product, along with new proofs and constructions in the theory of ∞-categories and ∞-operads.

Findings

Explicit formula for Segalification of n-fold simplicial spaces

New proof of invariance of right fibrations

Explicit construction of the Boardman-Vogt tensor product of ∞-operads

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.