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We show how concurrent quantales and concurrent Kleene algebras arise as convolution algebras Q^X of functions from structures X with two ternary relations that satisfy relational interchange laws into concurrent quantales or Kleene algebras Q. The elements of Q can be understood as weights; the case Q= corresponds to a powerset lifting. We develop a correspondence theory between relational properties in X and algebraic properties in Q and Q^X in the sense of modal and substructural logics, andarXiv:2002.02321v1 fatcat:dyjzozvmhzd75cmus2v6hhpwxa