A pasting theorem for iterated Segal spaces

TL;DR

This paper introduces a new formalism of pasting shapes for iterated Segal spaces and proves a corresponding pasting theorem, advancing the understanding of composition in higher categorical structures.

Contribution

It presents a novel notion of pasting shapes for iterated Segal spaces and establishes a new pasting theorem for these structures.

Findings

Pasting shapes classify arrangements of composing cells.

A new pasting theorem for iterated Segal spaces is proved.

Formalism enhances understanding of composition in higher categories.

Abstract

We introduce a novel notion of pasting shapes for iterated Segal spaces which classify particular arrangements of composing cells in d-uple Segal spaces. Using this formalism, we then continue to prove a pasting theorem for these iterated Segal spaces.