# On functorial (co)localization of algebras and modules over operads

## TL;DR

This paper establishes conditions ensuring that operadic algebras and modules are preserved under (co)localization functors, motivated by applications in motivic homotopy groups.

## Contribution

It provides general criteria for the preservation of operadic structures under (co)localization, extending previous results in homotopical algebra.

## Key findings

- Operadic algebras are preserved under certain (co)localization functors.
- Modules over operads maintain their structure after localization.
- Applications to motivic homotopy groups are demonstrated.

## Abstract

Motivated by calculations of motivic homotopy groups, we give widely attained conditions under which operadic algebras and modules thereof are preserved under (co)localization functors