Pushout: A Mathematical Model of Architectural Merger

Although there are many formal representations of architecture, actually determining what an architecture should be when systems are merged is largely based on context and human intuition. The goal of this paper is to find a mathematical model which supports this context and determines the architecture when the systems have been merged. A category of architectural models is presented, and the pushout in this category provides the unique minimal merger of two architectures by way of an abstraction of the desired intersection. We conclude by identifying deeper aspects of architectural type which should be incorporated into this theory, and how the whole model might be automated.