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This article provides an account of the functorial correspondence betweenirreducible singular $G$-monopoles on $S^1\times \Sigma$ and $\vec{t}$-stablemeromorphic pairs on $\Sigma$. The main theorem of [1] is thus generalized herefrom unitary to arbitrary compact, connected gauge groups. The requireddistinctions and similarities for unitary versus arbitrary gauge are clearlyoutlined and many parallels are drawn for easy transition. Once thecorrespondence theorem is complete, the spectral decomposition is addressed.

Singular $G$-monopoles on $S^1\times \Sigma$