We establish a Quillen equivalence relating the homotopy theory of Segal operads and the
homotopy theory of simplicial operads, from which we deduce that the homotopy coherent …

The homotopy theory of∞‐operads is defined by extending Joyal's homotopy theory of∞‐
categories to the category of dendroidal sets. We prove that the category of dendroidal sets …

We introduce the concept of a dendroidal set. This is a generalization of the notion of a
simplicial set, specially suited to the study of (coloured) operads in the context of homotopy …

We introduce the dendroidal analogues of the notions of complete Segal space and of Segal
category, and construct two appropriate model categories for which each of these notions …

This open access book offers a self-contained introduction to the homotopy theory of
simplicial and dendroidal sets and spaces. These are essential for the study of categories …

We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal
model categories gives rise to a Quillen equivalence between their model categories of (non …

We compare two approaches to the homotopy theory of∞-operads. One of them, the theory
of dendroidal sets, is based on an extension of the theory of simplicial sets and∞-categories …

This paper explores the relationship amongst the various simplicial and pseudosimplicial
objects characteristically associated to any bicategory C. It proves the fact that the geometric …

We present a definition of homotopy algebra for an operad, and explore its consequences.
The paper should be accessible to topologists, category theorists, and anyone acquainted …

We realise Joyal'cell category Θ as a dense subcategory of the category of ω-categories.
The associated cellular nerve of an ω-category extends the well-known simplicial nerve of a …