Connectivity, indecomposable, and weakly reversible in S-posets
Over the past four decades an extensive literature covered the properties of [Formula: see text]-acts. However, only few studies had generalized some known properties of [Formula: see text]-acts to the [Formula: see text]-posets. The reversible, and indecomposable properties in [Formula: see text]-posets have been addressed previously but connectivity has not been defined in [Formula: see text]-posets yet. Connectivity property was found to be related to those of reversibility and flatness in the category of [Formula: see text]-acts. The primary objective of this paper is to define connectivity in the category of [Formula: see text]-posets for both versions: ordered “poconnected” and unordered “connected”. Examples are presented to show the difference between the two versions. The relationship between connectivity with other properties such as reversibility, and indecomposability had also been investigated. We show that the poconnected in [Formula: see text]-posets is always indecomposable, but the inverse is not true. We also find that the weakly reversible is always connected and indecomposable. These relations among these properties in [Formula: see text]-posets are different from their corresponding relations in [Formula: see text]-acts.