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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.