镶嵌的商及相关超结构
Quotients of mosaics and related hyperstructures
中文总结 AI 辅助
该研究深入探讨镶嵌和半镶嵌的商，通过刻画有效同余给出构建商对象新方法，用于研究小群的显式商镶嵌，还证明了镶嵌范畴有自然原正合结构。
中文摘要 AI 辅助
这是对推广超群的超结构——镶嵌和半镶嵌的商的深入研究。这些范畴中的商推广了超群文献中先前研究的那些。我们通过根据其底层等价关系来刻画，描述了这些范畴中的有效同余。此刻画用于提供构建关于自同态作用的商对象的新方法，以及研究一些小群的显式商镶嵌。我们还表明镶嵌范畴具有自然的原正合结构。
英文摘要
This is a thorough study of quotients of hyperstructures that generalize hypergroups, namely mosaics and semimosaics. The quotients in these categories generalize those studied previously in the literature on hypergroups. We describe the effective congruences in these categories by characterizing them in terms of their underlying equivalence relation. This characterization is applied to provide new methods of constructing quotient objects modulo the action of endomorphisms, as well as to study explicit quotient mosaics of some small groups. We also show that the category of mosaics has a natural proto-exact structure.
