On involutive monoidal categories

J.M. Egger

In this paper, we consider a non-posetal analogue of the notion of involutive quantale; specifically, a (planar) monoidal category equipped with a covariant involution that reverses the order of tensoring. We study the coherence issues that inevitably result when passing from posets to categories; we also link our subject with other notions already in the literature, such as balanced monoidal categories and dagger pivotal categories.

Keywords: involutive monoidal categories, dagger pivotal categories, braidings, balances, coherence theorems

2000 MSC: 18D10,18D15

Theory and Applications of Categories, Vol. 25, 2011, No. 14, pp 368-393.

Published 2011-07-14.


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