Theoretical analysis demonstrates a generalization of the Milnor–Schwarz lemma for inverse monoids acting on presheaves of metric spaces, indicating new geometric links in semigroup theory.
We generalise the Milnor–Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, inspired by the arguments for group actions on metric spaces; the other involves a version of the Vietoris–Rips complex, and builds on work of Chung–Martínez–Szakács.
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Mangioni et al. (2026) studied this question.