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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-3,
author = {Jolanta S\l omi\'nska},
title = {Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {60},
year = {2012},
pages = {219-239},
zbl = {1255.18001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-3}
}
Jolanta Słomińska. Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 60 (2012) pp. 219-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba60-3-3/