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We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized   $F$  -structures on manifolds that are not necessarily global products. Using our Abstract Morimoto Theorem, we give a characterization of invariant generalized complex structures on products in which one factor is a Lie group. As a second application, we extend a theorem of Blair, Ludden and Yano on Hermitian bicontact manifolds to the non-commutative case.

AN ABSTRACT MORIMOTO THEOREM FOR GENERALIZED F -STRUCTURES