A $\mathbb{Z}/2\mathbb{Z}$-algebra \mathbb{Z}/2\mathbb{Z}$-graded algebra is said to supercommute if $xy = (-1)^{|x| |y|} yx$; in other words, odd elements anticommute. Why is this the "right" definition of supercommutativity? (Put another way, why is this the natural tensor product structure on super vector spaces?) Answers from both a categorical or physical point of view would be great.
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What is the conceptual significance of supercommutativity?A $\mathbb{Z}/2\mathbb{Z}$-algebra is said to supercommute if $xy = (-1)^{|x| |y|} yx$; in other words, odd elements anticommute. Why is this the "right" definition of supercommutativity? (Put another way, why is this the natural tensor product structure on super vector spaces?) Answers from both a categorical or physical point of view would be great.
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