  Deterministic reaction networks (RNs) are tools to model diverse biological
phenomena characterized by particle systems, when there are abundant number of
particles. Examples include but are not limited to biochemistry, molecular
biology, genetics, epidemiology, and social sciences. In this chapter we
propose a new type of decomposition of RNs, called fiber decomposition. Using
this decomposition, we establish lifting of mass-action RNs preserving
stationary properties, including multistationarity and absolute concentration
robustness. Such lifting scheme is simple and explicit which imposes little
restriction on the reaction networks. We provide examples to illustrate how
this lifting can be used to construct RNs preserving certain dynamical
properties.
