Hello, I still like to add some remarks. Category theory is one part of mathematics, and it should be treated not better, but not worse than others. It looks more important to me that categorical thinking becomes popular in other areas in mathematics. Some years ago, a functional analyst needed half an our to prove that homeomorphic Banach spaces have homemorphic duals, a simple consequence of the fact that all functors preserve isomorphisms. Another example from my own experience: People, who worked about orthomodular lattices noticed that they have no tensor product. So they tried to weaken the notions and ended up with effect algebras, but unfortunately they did not admit a tensor product either. Su people looked for other notions. But they had already shown that a tensor product of effect algebras exists if one admits 0=1; i.e. the tensor product my collapse. But because they did not admit this, they had to formulate their result more complicated. Later I saw that tensor products of orthomodular posets exist if one admits 0=1; the easy proof uses the Adjoint Functor Theorem and does not give much insight into the structure. It also seems to work for orthomodular lattices. My preference for orthomodular posets rather than lattices is also inspired by categorical thinking. The idempotents of an arbitrary ring with 1 form an orthomodular poset, and this construction yields a functor. This is the non-commutative analogue to the Boolean algebra of idempotents of an arbitrary ring. But most people were inspired by quantum dynamics and were looking for an abstraction for the set of projections of a Hilbert space. Here joins and meets exist (somehow accidentially) because projections correspond to closed subspaces. But they are not continuous and have no physical meaning in general. I think it is often better to look for functorial notions than to use ad-hoc-abtractions. Greetings Reinhard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]