正规扩张反射性的一个判据
A criterion for reflectiveness of normal extensions
摘要：
给出了容许Galois结构中正规扩张是反射的一个新的充分条件。然后我们证明了当X是Barr-正合S-原模范畴C的S-特殊对象的（原模）反射子范畴时，这个条件确实满足，这里S是C中的分裂满射平凡扩张类.在给出一些具体的例子之后，我们还研究了Barr-正合单位范畴与其交换核之间的连接，并证明了它是可容许的。
英文摘要：
We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when X is the (protomodular) reflective subcategory of S-special objects of a Barr-exact S-protomodular category C, where S is the class of split epimorphic trivial extensions in C. Next to some concrete examples where the criterion may be applied, we also study the adjunction between a Barr-exact unital category and its abelian core, which we prove to be admissible.
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