  In this paper we introduce the notion of $\mathcal I^{\mathcal K}$-Cauchy
function, where $\mathcal I$ and $\mathcal K$ are ideals on the same set. The
$\mathcal I^{\mathcal K}$-Cauchy functions are a generalization of $\mathcal
I^*$-Cauchy sequences and $\mathcal I^*$-Cauchy nets. We show how this notion
can be used to characterize complete uniform spaces and we study how $\mathcal
I^{\mathcal K}$-Cauchy functions and $\mathcal I$-Cauchy functions are related.
We also define and study $\mathcal I^{\mathcal K}$-divergence of functions.
