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The idea that gauge theory has 'surplus' structure poses a puzzle: in onemuch discussed sense, this structure is redundant; but on the other hand, it isalso widely held to play an essential role in the theory. In this paper, weemploy category-theoretic tools to illuminate an aspect of this puzzle. Weprecisify what is meant by 'surplus' structure by means of functorialcomparisons with equivalence classes of gauge fields, and then show that suchstructure is essential for any theory that represents a rich collection ofphysically relevant fields which are 'local' in nature.

Why surplus structure is not superfluous