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Frobenius algebras and homotopy fixed points of group actions on bicategories

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Jan Hesse, Christoph Schweigert, and Alessandro Valentino

We explicitly show that symmetric Frobenius structures on a
finite-dimensional, semi-simple algebra stand in bijection to homotopy
fixed points of the trivial SO(2)-action on the bicategory of
finite-dimensional, semi-simple algebras, bimodules and intertwiners.
The results are motivated by the 2-dimensional Cobordism Hypothesis for
oriented manifolds, and can hence be interpreted in the realm of
Topological Quantum Field Theory.

Keywords:
symmetric Frobenius algebras, homotopy fixed points, group actions
on bicategories

2010 MSC:
18D05

*Theory and Applications of Categories,*
Vol. 32, 2017,
No. 18, pp 652-681.

Published 2017-05-03.

http://www.tac.mta.ca/tac/volumes/32/18/32-18.pdf

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