We show that every internal biequivalence in a tricategory $T$ is part of a biadjoint biequivalence. We give two applications of this result, one for transporting monoidal structures and one for equipping a monoidal bicategory with invertible objects with a coherent choice of those inverses.
Keywords: biequivalence, biadjoint biequivalence, tricategory, monoidal bicategory
2000 MSC: Primary 18D05, 18D10 06F05, 06F07, 08B30
Theory and Applications of Categories, Vol. 26, 2012, No. 14, pp 349-384.
Published 2012-08-07.
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