The PARALLEL ALGEBRA of PROCESSES Span(Graph)
We have just described Cospan(Graph/A) as a sequential algebra. However if we take A
B instead of A, a cospan in Graph/(A×B) from X to Y consists of four morphisms of graphs: X → G, Y → G, G → A, and G → B, where here A and B are thought of as graphs with a single vertex, and edge sets being A and B respectively.
But this is exactly an example of a process as defined in the first post of this series. X and Y are the sequential interface, A and B the parallel interface. Such a process is in Cospan(Graph/(A
B)), the sequential algebra, but also in Span((X+Y)\Graph), the parallel algebra.Read more »
Labels: category theory, computing