An Obligation is an objective that is owned by the party for producing a specific (set of) result(s) that are to be used (consumed) by that party and/or other parties.
In the figure below, objectives Obj-1 is an obligations of Red towards Yellow. Also, objective Obj-Grn-k is an obligation of Green towards Red.
Figure 1: Chained Objectives - results produced in one objective are consumed in another
The figure shows four parties (Red, Yellow, Blue and Green) and their associated scopes of control. Within these, they own the objectives (the figure shows 6 objectives owned by red and one for each of the other parties). The figure in the top right hand corner of the rectangle that represents an objective, is the party that the owner of the objective expects to produce the objective's results. It is not necessary that such a party is known all the time (e.g. objective Obj-1a).
The arrows indicate that results produced to realize a certain objective (at the source of the arrow) are (to be) used to produce the results of another objective (at the end/tip of the arrow).
For more information, e.g. about how different parties interact in their roles of producer and consumer, we refer you to the Governance and Management pattern.