论文标题
内部群体类别的动作表示性
Action representability of the category of internal groupoids
论文作者
论文摘要
当$ \ mathbb c $是半阿伯式类别时，众所周知，$ \ mathbb c $中内部groupoids的类别$ \ mathsf {grpd}（\ mathbb c）$又是半阿贝尔人。确定同样的现象是否发生在半阿伯式的特性被代表的行动所代替时（从Borceux，Janelidze和Kelly的意义上）取代时，是否会发生相同的现象。 In the present article we give a sufficient condition for this to be true: in fact we prove that the category $\mathsf{Grpd}(\mathbb C)$ is a semi-abelian action representable algebraically coherent category with normalizers if and only if $\mathbb C$ is a semi-abelian action representable algebraically coherent category with normalizers.例如，该结果特别适用于群体类别中的内部类固醇类别，例如代数和共同霍普夫代数。
When $\mathbb C$ is a semi-abelian category, it is well known that the category $\mathsf{Grpd}(\mathbb C)$ of internal groupoids in $\mathbb C$ is again semi-abelian. The problem of determining whether the same kind of phenomenon occurs when the property of being semi-abelian is replaced by the one of being action representable (in the sense of Borceux, Janelidze and Kelly) turns out to be rather subtle. In the present article we give a sufficient condition for this to be true: in fact we prove that the category $\mathsf{Grpd}(\mathbb C)$ is a semi-abelian action representable algebraically coherent category with normalizers if and only if $\mathbb C$ is a semi-abelian action representable algebraically coherent category with normalizers. This result applies in particular to the categories of internal groupoids in the categories of groups, Lie algebras and cocommutative Hopf algebras, for instance.
