  The composition problem for shortest paths asks the following: given shortest
paths on weighted graphs M and N which share a common boundary, find the
shortest paths on their union. This problem is a crucial step in any algorithm
which uses the divide and conquer method to find shortest paths. This extended
abstract details how this problem may be understood categorically. Finding
shortest paths is represented by a functor and the composition problem asks to
find the value of this functor on a pushout using the values of the functor on
the components. Furthermore, we present an algorithm which solves the
composition problem for shortest paths. When implemented in Python, this
algorithm reduces the computation time for finding shortest paths by relying on
precompilation.
