Erratum

Proposition 2 is false as stated in the published version of James Owen Weatherall’s “Understanding Gauge” (Philosophy of Science 83, no. 5 [2016]: 1039–49). The functor $\tilde{F}$ defined on page 1046 is full and essentially surjective, but it is not faithful. The proposition should be amended to read:

Proposition 2*. $\tilde{F}$ forgets only stuff.

The original proof of proposition 2 establishes proposition 2*; only the part of the proof that seeks to establish faithfulness is faulty.

It is a direct consequence of proposition 2* that $\tilde{F}$ does not forget structure, since it is full. In this sense, the arguments of the article following proposition 2 go through without modification: EM₃ does not have “excess structure,” in the sense discussed in this article, relative to EM₁. On the other hand, the relationship reflected by proposition 2* indicates that these theories should not be viewed as equivalent and suggests that in fact EM₃ has less structure than EM₁. Weatherall defers further discussion of this situation to future work.

The author discovered the error on his own, but he is grateful to James Nguyen, Nic Teh, and Laura Wells, whose article “Why Surplus Structure Is Not Superfluous” (forthcoming in British Journal for Philosophy of Science) prompted him to revisit proposition 2, and to Thomas Barrett, Jeremy Butterfield, and Sarita Rosenstock for helpful discussions.