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 formula_3 be the space of paths of various length in a based space "X". Then the fibration formula_4 that sends each path to its end-point is a "G"-fibration with "G" the space of loops of various lengths in "X".