We explore local units in groupoids and their applications, suggesting definitions and structures.
We present and explore the notion of local units within a groupoid, and further extend this concept to e-groupoids, e-semigroupoids, and e-groups. We provide various examples and examine the properties associated with these structures. Furthermore, we propose two innovative definitions of an e-group and employ them to establish the notion of local units within a groupoid. Moreover, we introduce the concepts of pseudoideals and pseudofilters within an e-group, and demonstrate that the poset of local unit-sets in a groupoid forms a semilattice.
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Saeid et al. (2025) studied this question.
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