If "X" is an orbifold (or orbispace), choose a covering by open subsets from amongst the orbifold charts "f""i" : "V""i" formula_19 "U""i". Let "Y" be the abstract simplicial complex given by the nerve of the covering: its vertices are the sets of the cover and its "n"-simplices correspond to "non-empty" intersections "U""α" = "U""i"1 formula_40 ··· formula_40 "U""i""n". For each such simplex there is an associated group Γα and the homomorphisms "f""ij" become the homomorphisms "f"στ. For every triple ρ formula_21 σ formula_21 τ corresponding to intersections