# Coextension of scalars in operad theory

## TL;DR

This paper characterizes when the restriction functor between operadic algebras admits a right adjoint, based on a factorization condition for operations in the codomain operad.

## Contribution

It provides a necessary and sufficient condition for the existence of a right adjoint to the restriction functor in operad theory.

## Key findings

- Identifies a factorization axiom for operad maps
- Establishes criteria for adjoint functors in operad algebras
- Advances understanding of scalar extension in operad theory

## Abstract

The functor between operadic algebras given by restriction along an operad map generally has a left adjoint. We give a necessary and sufficient condition for the restriction functor to admit a right adjoint. The condition is a factorization axiom which roughly says that operations in the codomain operad can be written essentially uniquely as operations in arity one followed by operations in the domain operad.

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Source: https://tomesphere.com/paper/1906.12275