I see, some care must be taken when constructing a graph suitable for construction of a Free category.

When parallel paths are present in the graph the are assumed to be not equal unless there is an equation specifically stating otherwise.

The only exception to this rule is the case of the identity morphisms which have the implicit \\( id \circ id = id \\) equation.

When parallel paths are present in the graph the are assumed to be not equal unless there is an equation specifically stating otherwise.

The only exception to this rule is the case of the identity morphisms which have the implicit \\( id \circ id = id \\) equation.