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Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories

Volume 60 / 2012

Jolanta Słomińska Bulletin Polish Acad. Sci. Math. 60 (2012), 219-239 MSC: 18A25, 18G30, 18G15, 16E40. DOI: 10.4064/ba60-3-3

Abstract

The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as $\mathop {\rm Ext} ^*$ groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.

Authors

  • Jolanta SłomińskaFaculty of Mathematics and Information Sciences
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland
    e-mail

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