A low-energy Muon Collider (MC) offers unique opportunities to study the recently found Higgs boson. However, due to a relatively large beam emittance with moderate cooling in this machine, large-aperture high- field superconducting (SC) magnets are required. The magnets need also an adequate margin to operate at a large radiation load from the muon decay showers. General specifications of the SC dipoles and quadrupoles for the 125 GeV c.o.m. Higgs Factory with an average luminosity of ~2x10**31 cm-2s-1 are formulated. Magnet conceptual designs and parameters are reported. The impact of the magnet fringe fields on the beam dynamics as well as the IR and lattice magnet protection from radiation are also reported and discussed.
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