In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety Z̃ in a quiver variety, and show the following results: (1) The homology group of Z̃ is a representation of a symmetric Kac-Moody Lie algebra g, isomorphic to the tensor product V (λ1)⊗· · ·⊗V (λN ) of integrable highest weight modu...

A classical tensor product A⊗B of complete lattices A and B, consisting of all down-sets in A×B that are join-closed in either coordinate, is isomorphic to the complete lattice Gal(A,B) of Galois maps from A to B, turning arbitrary joins into meets. We introduce more general kinds of tensor products for closure spaces and for posets. They have the expected universal property for bimorphisms (se...