Operadic categories from the viewpoint of simplicial homotopy theory

Batanin and Markl introduced the general notion of operadic category
for the purpose of proving the duoidal Deligne conjecture. The
notion and the machinery they develop is powerful, but the
definition is not so easy to grasp at first sight, because it
involves many subtle conditions. I will explain a new approach to
operadic categories, developed with Michael Batanin and Mark Weber.
We show how to interpret all the axioms in terms of simplicial
identities. One benefit of this approach is that it makes it easy to
modify the axioms to get a notion which is invariant under
equivalence of categories. Another benefit is that the notion now
easily can be ported to the infinity-world.