Grassmann parity ($|X|\in \mathbb{Z}/2\mathbb{Z}$)

The parity grading records whether a homogeneous element has even or odd Grassmann degree. Homogeneous elements obey $XY=(-1{)}^{|X||Y|}YX$. An odd differential uses the graded Leibniz rule; this is the sign bookkeeping behind left-acting BRST differential calculations.