The classifying space of an inverse semigroup

TL;DR

This paper refines the understanding of the classifying space of an inverse semigroup by introducing right generalized inverse *-semigroups and characterizing presheaves over meet semilattices algebraically.

Contribution

It replaces *-semigroups with right generalized inverse *-semigroups in the description of the classifying space, providing a new algebraic perspective.

Findings

Refined Funk's description using right generalized inverse *-semigroups

Characterized presheaves of sets over meet semilattices algebraically as right normal bands

Enhanced the algebraic understanding of inverse semigroup classifying spaces

Abstract

We refine Funk's description of the classifying space of an inverse semigroup by replacing his *-semigroups by right generalized inverse *-semigroups. Our proof uses the idea that presheaves of sets over meet semilattices may be characterized algebraically as right normal bands.