Composition of Fibrations and Quantification

Dear All We know that if p and q are fibrations, then their composition p.q is a fibration. But what about quantification … that is if reindexing along every morphism has a right/left adjoint in p and q, then does reindexing along every morphism in p.q have a right/left adjoint? Under some circumstances? Thanks for any thoughts Neil [For admin and other information see: http://www.mta.ca/~cat-dist/ ]