#
Cohomology theory in 2-categories

##
Hiroyuki Nakaoka

Recently, symmetric categorical groups are used for the study of the
Brauer groups of symmetric monoidal categories. As a part of these
efforts, some algebraic structures of the 2-category of symmetric
categorical groups SCG are being investigated. In this paper, we
consider a 2-categorical analogue of an abelian category, in such a way
that it contains SCG as an example. As a main theorem, we construct a
long cohomology 2-exact sequence from any extension of complexes in such a
2-category. Our axiomatic and self-dual definition will enable us to
simplify the proofs, by analogy with abelian categories.

Keywords:
symmetric categorical group, 2-category, cohomology, exact sequence

2000 MSC:
18D05

*Theory and Applications of Categories,*
Vol. 20, 2008,
No. 16, pp 543-604.

http://www.tac.mta.ca/tac/volumes/20/16/20-16.dvi

http://www.tac.mta.ca/tac/volumes/20/16/20-16.ps

http://www.tac.mta.ca/tac/volumes/20/16/20-16.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/16/20-16.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/20/16/20-16.ps

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