October 19, 2025Open Access

Cloven operadic categories: An approach to operadic categories with cardinalities in finite unordered sets

Key Points

The introduction of operadic categories with finite set cardinalities highlights new equivalences.
This approach establishes connections between operads and algebras akin to earlier frameworks by Batanin and Markl.
Applications to operadic categories may advance understanding in graph mathematics and modular operads.
The findings open pathways for further research on clones within the category of modular operads.

Abstract

We introduce and study operadic categories with cardinalities in finite sets and establish conditions under which their associated theories of operads and algebras are equivalent to the standard framework introduced in 2015 by Batanin and Markl. Our approach is particularly natural in applications to the operadic category of graphs and the related category of modular operads and their clones. 28 pages

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Cite This Study

Martin Markl (Fri,) studied this question.

synapsesocial.com/papers/68f43ef4854d1061a58abee2 https://doi.org/https://doi.org/10.46298/compositionality-7-5