Distributive operadic categories

Michael Batanin – 3 August 2022

A distributive operadic category is a pair consisting of two operadic category structures on the same class of objects. They have different classes of morphisms, different cardinality functors and different fiber functors which are related by certain distributive law. This distributive law amounts basically to a distributive law between two skew monoidal structures on collections (due to Steve Lack) induced by two operadic structures.