A factorization of a Galois connection investigated earlier is used to give a definition of a connectedness-disconnectedness Galois connection that is free of the notion of constant morphism. A new notion ofN-fixed morphism with respect to a classNof monomorphisms is presented. This is used to characterize the connectedness-disconnectedness Galois connection in the case thatNis closed under the formation of pullbacks. Some closedness properties of these Galois connections are investigated.
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