Coextension of scalars in operad theory

Abstract

© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.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.