  Catalogs of refactoring have key importance in software maintenance and
evolution, since developers rely on such documents to understand and perform
refactoring operations. Furthermore, these catalogs constitute a reference
guide for communication between practitioners since they standardize a common
refactoring vocabulary. Fowler's book describes the most popular catalog of
refactorings, which documents single and well-known refactoring operations.
However, sometimes refactorings are composite transformations, i.e., a sequence
of refactorings is performed over a given program element. For example, a
sequence of Extract Method operations (a single refactoring) can be performed
over the same method, in one or in multiple commits, to simplify its
implementation, therefore, leading to a Method Decomposition operation (a
composite refactoring). In this paper, we propose and document a catalog with
eight composite refactorings. We also implement a set of scripts to mine
composite refactorings by preprocessing the results of refactoring detection
tools. Using such scripts, we search for composites in a representative
refactoring oracle with hundreds of confirmed single refactoring operations.
Next, to complement this first study, we also search for composites in the full
history of ten well-known open-source projects. We characterize the detected
composite refactorings, under dimensions such as size and location. We conclude
by addressing the applications and implications of the proposed catalog.
