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We study linear and hermitian representations of finite $C_2$-graded groups.We prove that the category of linear representations is equivalent to acategory of antilinear representations as an $\infty$-category. We also provethat the category hermitian representations, as an $\infty$-category, isequivalent to a category of usual representations.

Real Representations of $C_2$-Graded Groups: The Linear and Hermitian Theories