  Interchange theorems between minimization and integration are useful in
optimization, especially in optimal control and in stochastic optimization. In
this article, we establish a generalized minimization interchange theorem,
where integration is replaced by a monotone mapping between posets (partially
ordered sets). As an application, we recover, and slightly extend, classical
results from the literature, and we tackle the case of the Choquet integral.
Our result provides insight on the mechanisms behind existing interchange
results.
