论文标题
ABELIAN类别中N-阿贝尔类别的代表
Representation of n-abelian categories in abelian categories
论文作者
论文摘要
令$ \ Mathcal {M} $为小$ n $ -Abelian类别。我们表明，绝对纯群体有价值的函数的类别是$ \ Mathcal {m} $，用$ \ Mathcal {l} _2（\ Mathcal {M}，\ Mathcal {G}）$表示，是Abelian类别，是ABELIAN类别，$ \ Mathcal {M} $等于subcatemore $ \ MATHCAL {L} _2（\ Mathcal {M}，\ Mathcal {G}）$以$ n $ -kernels和$ n $ -cokernels的方式是$ \ Mathcal {l} _2 _2（\ nathcal {m Mathcal {M Mathcal}，cy cycal {g} $ { $ \ MATHCAL {M} $。这为$ n $ -Abelian类别的Freyd-Mitchell嵌入定理提供了更高维度的版本。
Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of absolutely pure group valued functors over $\mathcal{M}$, denote by $\mathcal{L}_2(\mathcal{M},\mathcal{G})$, is an abelian category and $\mathcal{M}$ is equivalent to a full subcategory of $\mathcal{L}_2(\mathcal{M},\mathcal{G})$ in such a way that $n$-kernels and $n$-cokernels are precisely exact sequences of $\mathcal{L}_2(\mathcal{M},\mathcal{G})$ with terms in $\mathcal{M}$. This gives a higher-dimensional version of the Freyd-Mitchell embedding theorem for $n$-abelian categories.
