Combinatorial and homotopical aspects of $E_n$-operads

TL;DR

This paper demonstrates that specific categorical operads can produce $E_n$-operads through geometric realization, using combinatorial methods that bypass complex topological assumptions.

Contribution

It introduces a combinatorial approach to constructing $E_n$-operads from categorical operads, avoiding traditional topological complexities.

Findings

Categorical operads can generate $E_n$-operads via geometric realization.

The approach simplifies existing constructions by removing topological assumptions.

Provides a combinatorial framework for understanding $E_n$-operads.

Abstract

We show that a certain class of categorical operads give rise to $E_n$-operads after geometric realization. The main arguments are purely combinatorial and avoid the technical topological assumptions otherwise found in the literature.