  We provide analogues of the results from [FMR11, CMMR13] in the reference
list (which correspond to the case $\kappa = \omega$) for arbitrary
$\kappa$-Souslin quasi-orders on any Polish space, for $\kappa$ an infinite
cardinal smaller than the cardinality of $\mathbb{R}$. These generalizations
yield a variety of results concerning the complexity of the embeddability
relation between graphs or lattices of size $\kappa$, the isometric
embeddability relation between complete metric spaces of density character
$\kappa$, and the linear isometric embeddability relation between (real or
complex) Banach spaces of density $\kappa$.
