  We introduce adjoint cyclotomic multiple zeta values and cyclotomic multiple
harmonic values. They are two variants of cyclotomic multiple zeta values,
closely related to each other. They arise as key tools for the study of
$p$-adic cyclotomic multiple zeta values. Moreover, cyclotomic multiple
harmonic values provide an adelic lift to a cyclotomic generalization of finite
multiple zeta values. We establish certain standard properties of these two
objects. We consider two types of properties : some related to double shuffle
relations, and some related to associator and Kashiwara-Vergne relations.
