18 citations · 52 across the 13 of their papers we have counts for
20 papers
A characterization of the spectral Lie operad
Max Blans, Gijs Heuts
In this paper we study the structure of the -category of spectral Lie algebras. We show that this -category admits an interesting symmetric monoidal structure, defi…
Chromatic Euler characteristics and duality for infinite groups
Gijs Heuts, Irakli Patchkoria
We study a family of generalizations of the notion of Euler characteristic of discrete groups (or of orbifolds, depending on one's perspective) indexed on the natural numbers. For…
On periodic homotopy and homology equivalences of spaces
Shaul Barkan, Gijs Heuts, Yuqing Shi
There are at least two ways to approach the homotopy theory of spaces `at chromatic height ': one may localize with respect to -homology or with respect to -periodic…
Poincaré-Birkhoff-Witt Theorems in Higher Algebra
Omar Antolín-Camarena, Lukas Brantner, Gijs Heuts
We extend the classical Poincaré-Birkhoff-Witt theorem to higher algebra by establishing a version that applies to spectral Lie algebras. We deduce this statement from a basic rela…
Koszul duality and a conjecture of Francis-Gaitsgory
Gijs Heuts
Koszul duality is a fundamental correspondence between algebras for an operad and coalgebras for its dual cooperad , built from using the…
Formality of -algebras and cochains on spheres
Gijs Heuts, Markus Land
We study the loop and suspension functors on the category of augmented -algebras. One application is to the formality of the cochain algebra of the -sphere. We sho…
Partition complexes and trees
Gijs Heuts, Ieke Moerdijk
We construct a homotopy initial functor from the partition complex of a finite set to a category of trees with leaves labelled by . As an application, this provides an equiv…
A short proof of the straightening theorem
Fabian Hebestreit, Gijs Heuts, Jaco Ruit
We provide a short and reasonably self-contained proof of Lurie's straightening equivalence, relating cartesian fibrations over a given -category with contravariant fun…
Lie algebra models for unstable homotopy theory
Gijs Heuts
Quillen showed how to describe the homotopy theory of simply-connected rational spaces in terms of differential graded Lie algebras. Here we survey a generalization of Quillen's re…
A Whitehead theorem for periodic homotopy groups
Tobias Barthel, Gijs Heuts, Lennart Meier
We show that -periodic homotopy groups detect homotopy equivalences between simply-connected finite CW-complexes.
Lie algebras and -periodic spaces
Gijs Heuts
We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in -periodic homotopy groups. The case n = 0 corresponds to rati…
Monadicity of the Bousfield-Kuhn functor
Rosona Eldred, Gijs Heuts, Akhil Mathew +1
We consider the localization of the -category of spaces at the -periodic equivalences, the case being rational homotopy theory. We prove that this localization i…
The -periodic Goodwillie tower on Wedges and Cofibres
Lukas Brantner, Gijs Heuts
We introduce general methods to analyse the Goodwillie tower of the identity functor on a wedge of spaces (using the Hilton-Milnor theorem) and on the cofibre $\mathrm{c…
Two models for the homotopy theory of -operads
Hongyi Chu, Rune Haugseng, Gijs Heuts
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…
Left fibrations and homotopy colimits II
Gijs Heuts, Ieke Moerdijk
For a small simplicial category A, we prove that the homotopy colimit functor from the category of simplicial diagrams on A to the category of simplicial sets over the homotopy-coh…
Goodwillie approximations to higher categories
Gijs Heuts
We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie…
Left fibrations and homotopy colimits
Gijs Heuts, Ieke Moerdijk
For a small category A, we prove that the homotopy colimit functor from the category of simplicial diagrams on A to the category of simplicial sets over the nerve of A establishes…
On the equivalence between Lurie's model and the dendroidal model for infinity-operads
Gijs Heuts, Vladimir Hinich, Ieke Moerdijk
We compare two approaches to the homotopy theory of infinity-operads. One of them, the theory of dendroidal sets, is based on an extension of the theory of simplicial sets and infi…
An infinite loop space machine for infinity-operads
Gijs Heuts
This paper describes a consequence of the more general results of a previous paper which is of independent interest. We construct a functor from the category of dendroidal sets, wh…
Algebras over infinity-operads
Gijs Heuts
We develop a notion of an algebra over an infinity-operad with values in infinity-categories which is completely intrinsic to the formalism of dendroidal sets. Its definition invol…