Promise Theory concerns the 'alignment', i.e. the degree of functional compatibility and the 'scaling' properties of process outcomes in agent-based models, with causality and intentional semantics. It serves as an umbrella for other theories of interaction, from physics to socio-economics, integrating dynamical and semantic concerns into a single framework. It derives its measures from sets, and can therefore incorporate a wide range of descriptive techniques, giving additional structure with predictive constraints. We review some structural details of Promise Theory, applied to Promises of the First Kind, to assist in the comparison of Promise Theory with other forms of physical and mathematical modelling, including Category Theory and Dynamical Systems. We explain how Promise Theory is distinct from other kinds of model, but has a natural structural similarity to statistical mechanics and quantum theory, albeit with different goals; it respects and clarifies the bounds of locality, while incorporating non-local communication. We derive the relationship between promises and morphisms to the extent that this would be a useful comparison.