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.