Universal derived equivalences of posets

Details Universal derived equivalences of posets Universal derived equivalences of posets

2007-05-07

arxiv.org/abs/0705.0946v2

Mathematics

Representation Theory

18 pages, added author's details

Scientific paper

By using only combinatorial data on two posets X and Y, we construct a set of so-called formulas. A formula produces simultaneously, for any abelian category A, a functor between the categories of complexes of diagrams over X and Y with values in A. This functor induces a triangulated functor between the corresponding derived categories. This allows us to prove, for pairs X, Y of posets sharing certain common underlying combinatorial structure, that for any abelian category A, regardless of its nature, the categories of diagrams over X and Y with values in A are derived equivalent.

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