Operadic 2-rigs
arXiv:2607.12705
summary
The paper introduces operadic 2‑rigs and proves that the bicategory of operads and bimodules embeds fully into the bicategory of symmetric 2‑rigs, showing this sub‑bicategory is the universal completion under Eilenberg‑Moore‑Kleisli objects.
Abstract
We show that the bicategory of operads and bimodules can be embedded into the bicategory of symmetric 2-rigs, a categorification of commutative rings. In order to do this, we introduce the notion of an operadic 2-rig and show that the full sub-bicategory of symmetric 2-rigs spanned by operadic 2-rigs has the universal property of being a completion under Eilenberg-Moore-Kleisli objects.
31 pages. Comments welcome
Topics & keywords
#operads#bicategories#2-rigs#symmetric monoidal categories#categorification#Eilenberg-Moore/Kleisli constructionsoperadic 2-rigsymmetric 2-rigoperads and bimodulesuniversal propertycompletionEilenberg-MooreKleisli objects