In algebraic topology, a G-fibration or principal fibration is a generalization of a principal G-bundle, just as a fibration is a generalization of a fiber bundle. By definition, given a topological monoid G, a G-fibration is a fibration p: P→B together with a continuous right monoid action P × G → P such that(1) for all x in P and g in G. (2) For each x in P, the map is a weak equivalence.