  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.
