Extending the Ehresmann-Schein-Nambooripad Theorem

The Ehresmann-Schein-Nambooripad Theorem for Inverse Categories

The Ehresmann-Schein-Nambooripad (ESN) Theorem asserts an equivalence between the category of inverse semigroups and the category of inductive groupoids. In this paper, we consider the category of inverse categories and functors -- a natural generalization of inverse semigroups -- and extend the ESN theorem to an equivalence between this category and the category of top-heavy locally inductive groupoids and locally inductive functors. From the proof of this extension, we also generalize the ESN Theorem to an equivalence between the category of inverse semicategories and the category of locally…

向双侧Ehresmann半群oids的Ehresmann-Schein-Nambooripad定理的推广

A Generalization of the Ehresmann-Schein-Nambooripad Theorem to Two-Sided Ehresmann Semigroupoids

本文提出双侧Ehresmann半群oids的概念，并将其与局部双序Ehresmann范畴相对应，从而推广了Ehresmann-Schein-Nambooripad定理。

关于左限制半群oid的Ehresmann-Schein-Nambooripad型定理

An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids

本文提出局部诱导星座的概念，建立了左限制半群oid与局部诱导星座的同构关系，并推广了一侧限制半群的结果。