Epimorphisms of compact groups are onto
Abstract: It is proved that the epimorphisms in the category of compact groups are surjective. The proof is based on the representation theory of compact groups, especially on the well-known fact, that for a closed proper subgroup of a compact group there exists an irreducible representation of which, when restricted to , contains the unit representation.
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Keywords: Epimorphisms, category, compact groups, finite-dimensional representations, unitary transformations
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