We construct a spectral sequence quite like $\check{\mathrm{C}}$ech-to-derived category spectral sequence for hypercoverings on \Delta S$, a small category constructed from, and slightly larger than,$\Delta$. In effect this gives a unified proof of old results and new— e.g.$C$a smooth projective curve of genus$g$, of unordered configuration spaces, of the moduli space of smooth sections of a fixed$\mathfrak{g}^r_d$that is$m$-very ample for some$m$, some geoemetric Batyrev--Manin type conjectures over global function fields for weighted projective stacks, complete simplicial toric varieties etc. In the special case when we have a monoid over a graded commutative ring our spectral sequence corresponds to that of the derived indecomposables (in the sense of Galatius--Kupers--Randal—Williams) giving an alternative topological interpretation of the moduli spaces above.