  In order to see the behavior of $\imath$canonical bases at $q = \infty$, we
introduce the notion of $\imath$crystals associated to an $\imath$quantum group
of certain quasi-split type. The theory of $\imath$crystals clarifies why
$\imath$canonical basis elements are not always preserved under natural
homomorphisms. Also, we construct a projective system of $\imath$crystals whose
projective limit can be thought of as the $\imath$canonical basis of the
modified $\imath$quantum group at $q = \infty$.
