JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 3, Pages 337 - 350
(December 2003)
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CATEGORIFYING
THE NONABELIAN BAR CONSTRUCTION
Lucian M. Ionescu (U. S. A.)
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Abstract: A categorification of
the nonabelian bar construction is obtained by
interpreting parity complexes as n-categories.
The categorical properties are applied to group
cohomology via parity quasi-complexes. In
particular, a parity homotopy is a natural
transformation between the functors associated
to morphisms of parity complexes.
As an application of
the above ideas group extensions are considered,
and Schreier theory reinterpreted.
Further
developments and applications to TQFTs from
state sums are considered. |
Keywords and phrases: homotopical
algebra, bar construction, nonabelian cohomology. |
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