In this paper we characterize bonds , as defined by Wille, by employing a less rigid set of axioms thus enabling the definition of the category BOND . Since bonds generalize Chu mappings we present a faithful functor between CHU and BOND . Moreover, we propose the Galois morphisms generalizing bonds; this allows us to define the category MGI . Lastly, we suggest a general method to construct categories of adjunctions from any given category. The category of adjunctions generated from the category of order-preserving Galois connections, named MGP , turns out to be equivalent to the category MGI .