Introduction

In this book we study a generalization of this construction with the aim to model functors on algebras over operads. For an operad P, we use the notation PE to refer to the category of P-algebras in E. We aim to model functors F : RE → E from a category of algebras over an operad R to the underlying category E, functors F : E → PE from the underlying category E to a category of algebras over an operad P, as well as functors F : RE → PE from a category of algebras over an operad R to another category of algebras over an operad P.