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the mapping is a fibration, where is the pullback and the projections of onto and yield the following commutative diagram:The fibration is called the pullback fibration or induced fibration.

Pathspace fibration

With the pathspace construction, any continuous mapping can be extended to a fibration by enlarging its domain to a homotopy equivalent space. This fibration is called pathspace fibration.

The total space of the pathspace fibration

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