High Quality Content by WIKIPEDIA articles! In mathematics, in particular the theory of principal bundles, one can ask if a G-bundle "comes from" a subgroup H < G. This is called reduction of the structure group (to H), and makes sense for any map H to G, which need not be an inclusion (despite the terminology).Formally, given a G-bundle B and a map H ? G (which need not be an inclusion), a reduction of the structure group (from G to H) is an H-bundle BH such that the pushout B_H times_H G is isomorphic to B.

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