# The configuration category of a product

## TL;DR

This paper introduces a construction based on operad theory that characterizes the configuration category of a product manifold using the configuration categories of its factors, bridging topology and algebraic structures.

## Contribution

It provides a novel operad-based framework to describe the configuration category of product manifolds from their individual configuration categories.

## Key findings

- Configuration category of a product manifold can be described via operad constructions.
- The approach relates the configuration categories of factors to that of the product.
- Operad theory offers a new perspective on manifold configuration spaces.

## Abstract

A construction related to the Boardman-Vogt tensor product of operads allows us to describe the configuration category of a product manifold $M\times N$ in terms of the configuration categories of the factors $M$ and $N$.