Cosheaf representations of relations and Dowker complexes

Abstract The Dowker complex is an abstract simplicial that constructed from a binary relation in straightforward way. Although there are two ways to perform this construction—vertices for the either rows or columns of matrix representing relation—the constructions homotopy equivalent. This article shows construction non-faithful covariant functor. Furthermore, we show functor can be made faithful by enriching into cosheaf on complex. summarized integer weight function complete isomorphism invariant relation. representation actually embodies both complexes, and construct duality exchanges complexes.