“…Here we get rid of the above restrictions in [5] and show that the result holds in arbitrary characteristic, for complexes of coherent sheaves, and most importantly, without the bound on dim k V . As a consequence we can show how various old and recent resolutions in the literature, the Eagon-Northcott complex, Buchsbaum-Rim and Buchsbaum-Eisenbud complexes [6, A2.6], pure resolutions of modules supported on determinantal varieties [9], and tensor complexes [25], may be obtained by the simple procedure of zipping the Tate resolutions of various vector bundles with supernatural cohomology on P(W ), or more generally locally Cohen-Macaulay sheaves, with an exterior coalgebra on V .…”