This paper concerns the old problem, whether every distributive algebraic lattice is isomorphic to the congruence lattice of a lattice. The author discovers a new approach to reduce the representation problem to investigations of congruence lattices of finite lattices. His approach is the following. Let D be the category of finite distributive lattices where the morphisms are the one-to-one 0-preserving \(\vee\)-homomorphism. Is there any functor R of D to the category of finite lattices with lattice embeddings such that the following holds? (i) For any distributive lattice D there is an isomorphism \(\phi_ D: D\cong Con(R(D)).\), (ii) If \(\delta\) : \(D_ 1\to D_ 2\) is a one-to-one 0- preserving \(\vee\)-homomorphism then \(R(D_ 1)\) has a lattice embedding R(\(\delta)\) to \(R(D_ 2)\) such that \(R(\delta_{12}\delta_{23})=R(\delta_{12})R(\delta_{23})\) for \(\delta_{12}: D_ 1\to D_ 2\) and \(\delta_{23}: D_ 2\to D_ 3.\), (iii) If Con(R(\(\delta)\)) is the mapping of \(Con(R(D_ 1))\) to \(Con(R(D_ 2))\) induced by R(\(\delta)\) then \(\phi_{D_ 2}\circ \delta =Con(R(\delta)\circ \phi_{D_ 1}\). If such a functor R exists then the representation problem would have a positive solution, namely every distributive semilattice D is the direct limit of its finite distributive subsemilattices, \(D_{\gamma}\)-s. Then the \(R(D_{\gamma})\)-s form a directed set whose direct limit L has the congruence lattice I(D), the ideal lattice of D. The author solves a modified program. He proves an analogous result for distributive lattices and 0-preserving lattice embeddings in the place of semilattices and \(\vee\)-embeddings. In this way the author gets a new proof for a theorem of the reviewer which states that every ideal lattice of a distributive lattice is isomorphic to the congruence lattice of a lattice [\textit{E. T. Schmidt}, Acta Sci. Math. 43, 153-168 (1981; Zbl 0463.06007)].