关于霍普夫代数的满态和单态
On epimorphisms and monomorphisms of Hopf algebras
摘要：
我们提供了域上霍普夫代数范畴中的非满同态$H\to K$的例子，即使有额外的要求，即$K$有双射对极，通过证明从一个霍普夫代数到它的包络霍普夫代数的泛映射是$\halg$中的满同态，尽管它不需要是满满射。对霍普夫代数范畴中的单态射是否必然内射的问题，得到了对偶结果.我们还注意到，这些自动成为霍普夫代数的非忠实平坦映射和非忠实共平坦映射的例子。
英文摘要：
We provide examples of non-surjective epimorphisms $H\to K$ in the category of Hopf algebras over a field, even with the additional requirement that $K$ have bijective antipode, by showing that the universal map from a Hopf algebra to its enveloping Hopf algebra with bijective antipode is an epimorphism in $\halg$, although it is known that it need not be surjective. Dual results are obtained for the problem of whether monomorphisms in the category of Hopf algebras are necessarily injective. We also notice that these are automatically examples of non-faithfully flat and respectively non-faithfully coflat maps of Hopf algebras.
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