  The Scarf complex for lattices is well understood and utilized. In 2014, the
author expanded the use of the term Scarf complex to encompass an infinite set
in $\mathbb{Z}^n$ that was generated via an action of a lattice
$\Lambda\in\mathbb{Z}^n$ upon a finite subset $A\subset\mathbb{N}^n$. This
paper aims to further generalize the use of Scarf complex by removing the
integer lattice completely while maintaining the essence of the Scarf complex.
