论文标题
关于单型单态的正态性
On the normality of monoid monomorphisms
论文作者
论文摘要
在单体类别中，我们表征了在适当意义上是正常的反身关系，预先定位或等价关系的单态性。此类内部关系的零类是用与之关联的方便句法关系来描述的，然后是通过与相应的归一化函数相关的辅助。这些附件引起的最大分类对等是其零级别产生的关系类别与单态性的类别之间的等价性，我们建议我们称之为{正常}的内部关系。尽管我们认为这个想法是横向到该领域文献的横向，但并未得到充分的一般性提出和探索。归一化函数的伴随的存在允许发展正常单态理论，因此将基团和原始类别类别的许多结果扩展到了单体和联合类别。
In the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-classes of such internal relations are first described in terms of convenient syntactic relations associated to them and then through the adjunctions associated with the corresponding normalization functors. The largest categorical equivalences induced by these adjunctions provide an equivalence between the categories of relations generated by their zero-classes and the ones of monomorphisms that we suggest to call {normal with respect to} the internal relations considered. This idea, although being transverse to the literature in the field, has not in our opinion been presented and explored in full generality. The existence of adjoints to the normalization functors permits developing a theory of normal monomorphisms, thus extending many results from groups and protomodular categories to monoids and unital categories.
