G-fibration

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

A principal G-bundle is a prototypical example of a G-fibration. Another example is Moore's [path space fibration]: namely, let be the space of paths of various length in a based space X. Then the fibration that sends each path to its end-point is a G-fibration with G the space of loops of various lengths in X.