  This paper solves partially a question suggested by Fontbona and M\'el\'eard
in a paper published in 2015. The issue is to obtain rigorously cross-diffusion
systems \`a la Shigesada-Kawasaki-Teramoto as the limit of relaxed systems in
which the cross-diffusion and reaction coefficients are non-local. We depart
from the existence result established by Fontbona M\'el\'eard for a general
class of non-local systems and study the corresponding asymptotic as the
convolution kernels tend to Dirac masses, but only in the case of (strictly)
triangular systems, with bounded coefficients. Our approach is based on a new
result of compactness for the Kolmogorov equation, which is reminiscent of the
celebrated duality lemma of Michel Pierre.
