Abstract. In this paper we propose the characterization of two new structures, the Agree Concept Lattice and the Quotient Agree Lattice of a database relation. Both of them are of great interest for multidimensional database analysis. They provide a formal framework which makes it possible to improve computation time, reduce representation and easily navigate through the Hasse diagram. These structures are generic, apply to various database analysis problems and combine formal concept analysis and database theory. They make use of the concepts of agree set and database partition. Agree set and partition are associated to define the Agree Concept of a database relation. The set of all the Agree Concepts is organized within the Agree Concept Lattice. The Quotient Agree Lattice is along the lines of both the Titanic framework and the quotient cube.We also briefly present three application fields of the proposed structures. The first two ones are classical since they concern on the one hand the discovery of functional and approximate dependencies for database design and tuning and on the other hand the data cube computation and representation. The latter field has been recently investigated. The underlying issue is to retrieve the most relevant objects according to the user expectations: the Skyline. The multidimensional generalization of the Skyline has been proposed through the Skycube. The proposed structures smartly solve the problem of partial materialization of Skycube with reconstruction guarantee.