In this talk we report on our study of two-colour lattice QCD with N_f=4 staggered fermion degrees of freedom with equal electric charge q in a homogeneous magnetic field B at non-zero temperature T. We find indications for a non-monotonic behaviour of the critical temperature as a function of the magnetic field strength and, as a consequence, for the occurence of `inverse magnetic catalysis within the transition region for magnetic fields in the range 0 < qB < 0.7 GeV^2.
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