Local units in groupoids

Abstract

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.