In this paper we consider the category of squarefree modules over the polynomial ring and an exact duality functor, which is an extension of the Alexander dual of a simplicial complex. We give a relationship between the squarefree components of local cohomology groups of a squarefree module and the Tor groups of its dual. With this result it is shown that a squarefree module is sequentially Cohen–Macaulay if and only if the dual is componentwise linear.
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