PROPs for involutive monoids and involutive bimonoids

Daniel Graves

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.

Published 2020-09-22.

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