  Many features of physical systems, both qualitative and quantitative, become
sharply defined or tractable only in some limiting situation. Examples are
phase transitions in the thermodynamic limit, the emergence of classical
mechanics from quantum theory at large action, and continuum quantum field
theory arising from renormalization group fixed points. It would seem that few
methods can be useful in such diverse applications. However, we here present a
flexible modeling tool for the limit of theories: soft inductive limits
constituting a generalization of inductive limits of Banach spaces. In this
context, general criteria for the convergence of dynamics will be formulated,
and these criteria will be shown to apply in the situations mentioned and more.
