The category of involutive non-commutative sets encodes the structure of an involution compatible with a (co)associative (co)multiplication. We prove that the category of involutive bimonoids in a symmetric monoidal category is equivalent to the category of algebras over a PROP constructed from the category of involutive non-commutative sets.
Keywords: involutive non-commutative sets, bimonoid, bialgebras, PROP, symmetric monoidal categories
2020 MSC: 16T10, 18M05, 18M85
Theory and Applications of Categories, Vol. 35, 2020, No. 42, pp 1564-1575.