A bstract We resolve the existence of mixed ’t Hooft anomalies between the electric and magnetic (solitonic) symmetries in σ -models and gauge theories. We identify the anomaly as naturally originating from a higher group in the Whitehead tower of the target space. In particular, the magnetic charges (topological solitons) can be interpreted as higher connections on the stages of the Whitehead tower, when pulled back to spacetime. This allows us to derive the form of the ( d + 1)-dim topological