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	Volume 3, Issue 3 Pg 337 - 505 (December 2003)
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JP Journal of Algebra, Number Theory and Applications

JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 3, Pages 337 - 350 (December 2003)

CATEGORIFYING THE NONABELIAN BAR CONSTRUCTION
Lucian M. Ionescu (U. S. A.)

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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P-ISSN: 0972-5555

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