逆范畴的Ehresmann-Schein-Nambooripad定理
The Ehresmann-Schein-Nambooripad Theorem for Inverse Categories
摘要：
Ehresmann-Schein-Nambooripad（ESN）定理证明了逆半群范畴和归纳群胚范畴之间的等价性。在本文中，我们考虑的范畴的逆范畴和函子-逆半群的一个自然推广-和ESN定理推广到这个范畴和范畴的top-heavy局部归纳群胚和局部归纳函子之间的等价。从这个推广的证明出发，我们还将ESN定理推广到逆半范畴与局部归纳群胚范畴之间的等价性，以及具有oplax函子的逆范畴与top-heavy局部归纳群胚和序函子范畴之间的等价性.
英文摘要：
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 inductive groupoids and to an equivalence between the category of inverse categories with oplax functors and the category of top-heavy locally inductive groupoids and ordered functors.
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