  In this paper, we discuss a connection between different linearizations for
non-abelian analogs of the second Painlev\'e equation. For each of the analogs,
we listed the pairs of the Harnard-Tracy-Widom (HTW), Flaschka-Newell (FN), and
Jimbo-Miwa (JM) types. A method for establishing the HTW-JM correspondence is
suggested. For one of the non-abelian analogs, we derive the corresponding
non-abelian generalizations of the monodromy surfaces related to the FN- and
JM-type linearizations. A natural Poisson structure associated with these
monodromy surfaces is also discussed.
