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 (1) p ( x g ) = p ( x ) {\displaystyle p(xg)=p(x)} for all x in P and g in G. (2) For each x in P, the map G → p − 1 ( p ( x ) ) , g ↦ x g {\displaystyle G\to p^{-1}(p(x)),g\mapsto xg} is a weak equivalence.