Complexes and their Sheaves

Arthur Knoebel ()

Chapter IV in Sheaves of Algebras over Boolean Spaces, 2012, pp 79-107 from Springer

Abstract: Abstract One easily generalizes the notion of complex, already known in module theory, to universal algebra, where it is new. A complex is an algebra equipped with a binary operation satisfying axioms analogous to those of a metric spaceTo represent an algebra is to decompose it into simpler parts, that is, to turn elements of an algebra into sequences whose components are elements in simpler algebras. Not all sequences are needed, and a simple criterion is desired for determining membership. This leads to the notion of sheaf. Its advantage is that the admissible sequences are certain continuous functions, called global sections.From complexes, sheaves are constructed, and the given algebra is isomorphic to a subalgebra of the algebra of global sections. The process may be reversed, from sheaves to complexes. This passage between complexes and sheaves is a categorical adjunction.

Keywords: Disjoint Union; Base Space; Natural Transformation; Global Section; Subdirect Product (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-4642-4_4

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