MATH.16:5.3 - Two views of one quantity

A model has candidate states A and B for two component descriptions. Each description specifies the value of a shared quantity in C. For example, the two ends of an ideal connection may be required to have equal potential.

The product contains arbitrary state pairs. Requiring agreement selects the pullback of the two quantity maps. Its projections retain both component states, so a later calculation can still use their other quantities.

The physical account must justify the ideal connection and the meaning of that potential. If the connection has a relevant drop, the equality premise changes. A relation involving the drop and other quantities must be modeled before constructing its compatible states. The mathematical construction supplies the combination once that relation has been formulated; it does not choose the physical interaction law.