双幺半群类的Ehresmann-Schein-Nambooripad定理
Ehresmann-Schein-Nambooripad theorems for classes of biunary semigroups
AI总结：
本研究得到一类广泛双幺半群的ESN定理，用带恒等元双作用的小范畴表示，推广已有相关工作，得到范畴同构且涵盖多类半群实例。
摘要：
我们得到了一类非常广泛的、具有幂等元值域的定义域和值域运算的双幺半群的ESN定理，用带有恒等元的适当双作用的小范畴来表示它们。我们的结果推广了Fitzgerald和Kinyon最近将可局部化半群转录范畴联系起来的工作，也推广了Lawson将Ehresmann半群与具有Ehresmann双作用的范畴联系起来的工作。与大多数ESN定理的研究方法不同，我们不要求范畴是有序的，也不要求它们的恒等元集具有任何特定结构。整个研究中，双幺半群用范畴而非任何形式的广义范畴来表示，我们得到了半群类与其相关富化范畴之间的范畴同构，而非范畴等价。我们的结果涵盖了Jones和王守峰所研究的DRC-半群类，同时也涵盖了并非两个同余条件都成立的情况，例如集合上的二元关系半群在配备定义域和值域运算的恶魔合成下的例子。
英文摘要：
We obtain an ESN theorem for a very general class of biunary semigroups with idempotent-valued domain and range operations, representing them in terms of small categories equipped with a suitable biaction of the identities on the category. Our results generalise the recent work of Fitzgerald and Kinyon connecting localisable semigroups to transcription categories, as well as that of Lawson linking Ehresmann semigroups to categories with Ehresmann biaction. In contrast to most approaches to ESN theorems, we do not require the categories to be ordered or for their sets of identities to possess any particular structure. Throughout, the biunary semigroups are represented using categories rather than generalised categories of any kind, and we obtain category isomorphisms between the clesses of semigroups and their associated enriched categories, rather than category equivalences. Our results cover the class of DRC-semigroups considered by Jones and Shoufeng Wang, but they also cover cases where not both congruence conditions hold, including examples such as the semigroup of binary relations on a set under demonic composition equipped with domain and range operations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
