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We extend Tilson's theory of the algebra of finite categories, in particular, the Derived Category Theorem, to the setting of forest algebras. As an illustration of the usefulness of this method, we provide a new proof of a result of Place and Segoufin characterizing locally testable tree languages.arXiv:1801.04337v1 fatcat:2ofmsya3w5dphbybv3wzdtvype