Talk:Concept lattice

N-dimensional? No
Actually, concept lattices are part of concept theory, a subject introduced by R. Wille in the context of AI applications, and they have nothing to do with dimension. Rather concept lattices arise from any relation (mathematics) in the same way that $$g rho x$$ if $$g.x = x$$ (fixed point under a group action) leads to the elementary Galois duality in (the trivial part of) Galois theory. In general, concept theory can be useful in order to clearly appreciate that many relations in mathematics like orthogonality, etc., automatically give rise to a dual lattice which is often of genuine interest. In interesting applications there are deeper facts about these lattices which must be proven using ideas outside concept theory itself.

I can write a more extensive WP article when I have time, based on the expository article I wrote when I was a graduate student. ---CH 23:10, 16 February 2006 (UTC)