This research introduces isomorphisms between left restriction semigroupoids and locally inductive constellations, implying broader applications for restriction categories.
We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellations. This construction offers an alternative to the celebrated Ehresmann–Schein–Nambooripad (ESN) Theorem and, in particular, generalizes results for one-sided restriction semigroups. We also obtain ESN-type theorems for one-sided restriction categories and inverse semigroupoids.
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Haag et al. (2026) studied this question.
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