Associahedra and Weak Monoidal Structures on Categories

TL;DR

This paper explores the algebraic structures on categories that correspond to $A_n$ structures on the geometric realization of their nerve, linking category theory with algebraic topology.

Contribution

It establishes a correspondence between algebraic structures on categories and $A_n$ structures on their nerve's geometric realization.

Findings

Identifies the algebraic structures corresponding to $A_n$ structures.

Provides a framework connecting category theory and algebraic topology.

Clarifies the relationship between categorical structures and geometric realizations.

Abstract

This paper answers the following question: what algebraic structure on a category corresponds to an $A_n$ structure (in the sense of Stasheff) on the geometric realization of its nerve?