Английская Википедия:G-fibration
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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,[1] 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) <math>p(x g) = p(x)</math> for all x in P and g in G.
- (2) For each x in P, the map <math>G \to p^{-1}(p(x)), g \mapsto xg</math> is a weak equivalence.
A principal G-bundle is a prototypical example of a G-fibration. Another example is Moore's path space fibration: namely, let <math>P'X</math> be the space of paths of various length in a based space X. Then the fibration <math>p: P'X \to X</math> that sends each path to its end-point is a G-fibration with G the space of loops of various lengths in X.
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