  A totally geodesic map $f:\mathcal X_1\to\mathcal X_2$ between Hermitian
symmetric spaces is tight if its image contains geodesic triangles of maximal
area. Tight maps were first introduced in [BIW09], and were classified in
[Ham13, Ham14, HO14] in the case of irreducible domain. We complete the
classification by analyzing also maps from reducible domains. This has
applications to the study of maximal representations and of the Hitchin
component for representations in the groups $Sp(2n,\mathbb R)$.
