PROPs for involutive monoids and involutive bimonoids

Abstract

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.

12 pages. Published in Theory and Applications of Categories. Major revision of the previous version. Theorems are now stated in a more general context

Cited by in corpus (3)

• Hyperoctahedral Homology for Involutive Algebras
• Reflexive homology
• Categorifying equivariant monoids