13 citations · 61 across the 20 of their papers we have counts for
23 papers
Derived plethystic algebra
Benjamin Antieau, Edith Hübner, Dmitry Kubrak +1
We prove comparison results about -categories of derived commutative rings with extra algebraic structure. For example, we show that several notions of derived -rings ag…
Symmetries and Higher-Form Connections in Derived Differential Geometry
Severin Bunk, Lukas Müller, Joost Nuiten +1
We introduce a general definition of higher-form connections on principal -bundles in differential geometry. This is achieved by developing the formal differentiation and i…
Theta-Categories and Tannakian duality
Joost Nuiten, Bertrand Toen
We introduce a notion of -categories, which is a refinement of the notion of symmetric monoidal -categories. We use this notion to prove a Tannakian duality statement, r…
Formal Integration of Derived Foliations
Lukas Brantner, Kirill Magidson, Joost Nuiten
Frobenius' theorem in differential geometry asserts that every involutive subbundle of the tangent bundle of a manifold integrates to a decomposition of into smooth leaves.…
Modeling -categories with Segal spaces
Lyne Moser, Joost Nuiten
In this paper, we construct a model structure for -categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show t…
On straightening for Segal spaces
Joost Nuiten
The straightening-unstraightening correspondence of Grothendieck--Lurie provides an equivalence between cocartesian fibrations between -categories and diagrams of $(\i…
PD Operads and Explicit Partition Lie Algebras
Lukas Brantner, Ricardo Campos, Joost Nuiten
Infinitesimal deformations are governed by partition Lie algebras. In characteristic , these higher categorical structures are modelled by differential graded Lie algebras, but…
Lie algebroids are curved Lie algebras
Damien Calaque, Ricardo Campos, Joost Nuiten
We show that there is an equivalence of -categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the -cate…
On k-invariants for -categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
Every -category can be approximated by its tower of homotopy -categories. In this paper, we prove that the successive stages of this tower are classified by k-…
Two-variable fibrations, factorisation systems and -categories of spans
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We prove a universal property for -categories of spans in the generality of Barwick's adequate triples, explicitly describe the cocartesian fibration corresponding to the s…
Lax monoidal adjunctions, two-variable fibrations and the calculus of mates
Rune Haugseng, Fabian Hebestreit, Sil Linskens +1
We provide a calculus of mates for functors to the -category of -categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformat…
Moduli problems for operadic algebras
Damien Calaque, Ricardo Campos, Joost Nuiten
A theorem of Pridham and Lurie provides an equivalence between formal moduli problems and Lie algebras in characteristic zero. We prove a generalization of this correspondence, rel…
An extension of Quillen's Theorem B
Ieke Moerdijk, Joost Nuiten
We prove a general version of Quillen's Theorem B, for actions of simplicial categories, in an arbitrary left Bousfield localization of the homotopy theory of simplicial presheaves…
Quillen cohomology of -categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
In this paper we study the homotopy theory of parameterized spectrum objects in the -category of -categories, as well as the Quillen cohomology of an $(\infty,…
The tangent bundle of a model category
Yonatan Harpaz, Joost Nuiten, Matan Prasma
This paper studies the homotopy theory of parameterized spectrum objects in a model category from a global point of view. More precisely, for a model category satisfy…
Koszul duality for Lie algebroids
Joost Nuiten
This paper studies the role of dg-Lie algebroids in derived deformation theory. More precisely, we provide an equivalence between the homotopy theories of formal moduli problems an…
Homotopical algebra for Lie algebroids
Joost Nuiten
We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and -algebroids over a commutative dg-algebra in characteristic zero. This al…
Localizing infinity-categories with hypercovers
Joost Nuiten
Given an -category with a set of weak equivalences which is stable under pullback, we show that the mapping spaces of the corresponding localization can be described as gro…
The abstract cotangent complex and Quillen cohomology of enriched categories
Yonatan Harpaz, Joost Nuiten, Matan Prasma
In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomol…
Tangent categories of algebras over operads
Yonatan Harpaz, Joost Nuiten, Matan Prasma
Associated to a presentable -category and an object is the tangent -category , consisting of parameteriz…
Minimal fibrations of dendroidal sets
Ieke Moerdijk, Joost Nuiten
We prove the existence of minimal models for fibrations between dendroidal sets in the model structure for infinity-operads, as well as in the covariant model structure for algebra…
Bohrification of local nets
Joost Nuiten
Recent results by Spitters et. al. suggest that quantum phase space can usefully be regarded as a ringed topos via a process called Bohrification. They show that quantum kinematics…
Bohrification of local nets of observables
Joost Nuiten
Recent results by Spitters et. al. suggest that quantum phase space can usefully be regarded as a ringed topos via a process called Bohrification. They show that quantum kinematics…