We generalise the concepts introduced by Baez and Dolan to define opetopes constructed from symmetric operads with a category, rather than a set, of objects. We describe the category of 1-level generalised multicategories, a special case of the concept introduced by Hermida, Makkai and Power, and exhibit a full embedding of this category in the category of symmetric operads with a category of o...

The operad Lie can be constructed as the operad of primitives PrimAs from the operad As of associative algebras. This is reflected by the theorems of Friedrichs, Poincaré-Birkhoff-Witt and Cartier-Milnor-Moore. We replace the operad As by families of free operads P, which include the operad Mag freely generated by a noncommutative non-associative binary operation and the operad of Stasheff poly...

We give an explicit description of the rigidification $\infty$-operad as a simplicial operad. This is based on notion dendroidal necklace, extending work Dugger and Spivak from categorical context to operadic context, although with different framework, which relates constructions involving necklaces standard factorization maps in category trees.

This work presents a detailed analysis of the combinatorics modular operads. These are operad-like structures that admit contraction operation as well an operadic multiplication. Their governed by graphs cycles, and known for their complexity. In 2011, Joyal Kock introduced powerful graphical formalism paper extends work. A monad operads is constructed corresponding nerve theorem proved, using ...