Tensor products and relation quantales

  title={Tensor products and relation quantales},
  author={M. Ern{\'e} and J. Picado},
  journal={Algebra universalis},
A classical tensor product $${A \otimes B}$$A⊗B of complete lattices A and B, consisting of all down-sets in $${A \times B}$$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 (separately continuous maps or maps preserving restricted joins in the… Expand
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