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We prove a higher-dimensional version of the Freyd-Mitchell embedding theorem for n-abelian categories. More precisely, for a positive integer nand a small n-abelian category M, we show that Mis equivalent to a full subcategory of an abelian category L2(M, G), where L2(M, G)is the category of absolutely pure group valued functors over M. We also show that n-kernels and n-cokernels in Mare precisely exact sequences of L2(M, G)with terms in M.
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