113 citations · 354 across the 32 of their papers we have counts for
36 papers
Free fibrations, lax colimits and Kan extensions for -categories
Fernando Abellán, Rune Haugseng, Louis Martini
In the first part of this paper we study fibrations of -categories. We give a simple characterization of such fibrations in terms of a certain square being a pullback,…
Normed equivariant ring spectra and higher Tambara functors
Bastiaan Cnossen, Rune Haugseng, Tobias Lenz +1
In this paper we extend equivariant infinite loop space theory to take into account multiplicative norms: For every finite group , we construct a multiplicative refinement of th…
Straightening for lax transformations and adjunctions of -categories
Fernando Abellán, Andrea Gagna, Rune Haugseng
We prove an unstraightening result for lax transformations between functors from an arbitrary -category to that of -categories. We apply this to study parti…
Homotopical commutative rings and bispans
Bastiaan Cnossen, Rune Haugseng, Tobias Lenz +1
We prove that commutative semirings in a cartesian closed presentable -category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors fr…
Higher categories
Rune Haugseng
Invited contribution to the Encyclopedia of Mathematical Physics. We give an introduction to the homotopical theory of higher categories, focused on motivating the definitions of t…
On the tensor product of enriched -categories
Rune Haugseng
We show that the tensor product of -categories enriched in a suitable monoidal -category preserves colimits in each variable, fixing a mistake in an earlier paper o…
Some remarks on higher Morita categories
Rune Haugseng
We take another look at the construction of double -categories of algebras and bimodules and prove a few supplemental results about these, including a simpler proof of the…
Enriched homotopy-coherent structures
Hongyi Chu, Rune Haugseng
We introduce a general notion of enrichment for homotopy-coherent algebraic structures described by Segal conditions, using the framework of "algebraic patterns" developed in our p…
From analytic monads to -operads through Lawvere theories
Rune Haugseng
We show that Lurie's model for -operads (or more precisely a "flagged" or "pinned" version thereof) is equivalent to the analytic monads previously studied by Gepner, Kock,…
Envelopes for Algebraic Patterns
Shaul Barkan, Rune Haugseng, Jan Steinebrunner
We generalize Lurie's construction of the symmetric monoidal envelope of an -operad to the setting of algebraic patterns. This envelope becomes fully faithful when sliced o…
The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory
Damien Calaque, Rune Haugseng, Claudia Scheimbauer
We construct a family of oriented extended topological field theories using the AKSZ construction in derived algebraic geometry, which can be viewed as an algebraic and topological…
-operads as symmetric monoidal -categories
Rune Haugseng, Joachim Kock
We use Lurie's symmetric monoidal envelope functor to give two new descriptions of -operads: as certain symmetric monoidal -categories whose underlying symmetric mo…
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…
On distributivity in higher algebra I: The universal property of bispans
Elden Elmanto, Rune Haugseng
Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of (-)categorie…
On (co)ends in -categories
Rune Haugseng
In this short note we prove that two definitions of (co)ends in -categories, via twisted arrow -categories and via -categories of simplices, are equivalent.…
Free algebras through Day convolution
Hongyi Chu, Rune Haugseng
Building on the foundations in our previous paper, we study Segal conditions that are given by finite products, determined by structures we call cartesian patterns. We set up Day c…
On lax transformations, adjunctions, and monads in -categories
Rune Haugseng
We use the basic expected properties of the Gray tensor product of -categories to study (co)lax natural transformations. Using results of Riehl-Verity and Zaganidis we…
Algebras for enriched -operads
Rune Haugseng
Using the description of enriched -operads as associative algebras in symmetric sequences, we define algebras for enriched -operads as certain modules in symmetric…
Homotopy-coherent algebra via Segal conditions
Hongyi Chu, Rune Haugseng
Many homotopy-coherent algebraic structures can be described by Segal-type limit conditions determined by an "algebraic pattern", bywhich we mean an -category equipped with…
Shifted Coisotropic Correspondences
Rune Haugseng, Valerio Melani, Pavel Safronov
We define (iterated) coisotropic correspondences between derived Poisson stacks, and construct symmetric monoidal higher categories of derived Poisson stacks where the -morphism…
Segal spaces, spans, and semicategories
Rune Haugseng
We show that Segal spaces, and more generally category objects in an -category , can be identified with associative algebras in the double -category of…
-Operads as Analytic Monads
David Gepner, Rune Haugseng, Joachim Kock
We develop an -categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new mo…
-operads via symmetric sequences
Rune Haugseng
We construct a generalization of the Day convolution tensor product of presheaves that works for certain double -categories. Using this construction, we obtain an -…