Rigidification of dendroidal infinity-operads

Enriched infinity operads

Two Models for the Homotopy Theory of ∞-operads

We compare two models for ∞-operads: the complete Segal operads of Barwick and the complete dendroidal Segal spaces of Cisinski and Moerdijk. Combining this with comparison results already in the literature, this implies that all known models for ∞-operads are equivalent — for instance, it follows that the homotopy theory of Lurie’s ∞-operads is equivalent to that of dendroidal sets and that of...

A Dendroidal Process Calculus

The Dendroidal Process Calculus (DPC) is designed as a new theory for modeling concurrent and distributed computations and systems, equipped with a non-sequential and compositional semantics. In this theory, a parallel composition is parameterized by a graph at the vertices of which subprocesses are located. Communication is allowed only between subprocesses related by an edge in this graph. Mo...

Rigidification of Quasi-categories

We give a new construction for rigidifying a quasi-category into a simplicial category, and prove that it is weakly equivalent to the rigidification given by Lurie. Our construction comes from the use of necklaces, which are simplicial sets obtained by stringing simplices together. As an application of these methods, we use our model to reprove some basic facts from [L] about the rigidification...

Constructions of En operads

Throughout this talk I will use the following conventions and notations. I will primarily consider operads in the category of compactly generated Hausdorff topological spaces having the homotopy type of CW-complexes. When I refer to simplicial operads or operads in the category of posets, it will be understood that they can be converted to topological operads by taking geometric realization or ...