273 citations · 767 across the 23 of their papers we have counts for
7 papers · 1 filter
The universal coCartesian fibration
Denis-Charles Cisinski, Hoang Kim Nguyen
We give a new proof of the straightening/unstraightening correspondence by proving a generalization of the univalence property of the universal coCartesian fibration.
Multitensor lifting and strictly unital higher category theory
Michael Batanin, Denis-Charles Cisinski, Mark Weber
In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first princ…
The Lifting Theorem for Multitensors
Michael Batanin, Denis-Charles Cisinski, Mark Weber
We continue to develop the theory of monads and multitensors. The central result of this paper - the lifting theorem for multitensors - enables us to see the Gray tensor product of…
Dendroidal Segal spaces and infinity-operads
Denis-Charles Cisinski, Ieke Moerdijk
We introduce the dendroidal analogs of the notions of complete Segal space and of Segal category, and construct two appropriate model categories for which each of these notions cor…
Algebras of higher operads as enriched categories II
Michael Batanin, Denis-Charles Cisinski, Mark Weber
One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work…
Dendroidal sets as models for homotopy operads
Denis-Charles Cisinski, Ieke Moerdijk
The homotopy theory of infinity-operads is defined by extending Joyal's homotopy theory of infinity-categories to the category of dendroidal sets. We prove that the category of den…