English
Related papers

Related papers: Equivariant dendroidal Segal spaces and $G$-$\inft…

200 papers

For a discrete colored operad $P$, we construct an adjunction between the category of dendroidal sets over the nerve of $P$ and the category of simplicial $P$-algebras, and prove that when $P$ is $\Sigma$-free it establishes a Quillen…

Algebraic Topology · Mathematics 2025-03-17 Francesca Pratali

In a previous paper we lifted Charles Rezk's complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of "relative categories," and our aim in this successor paper is to obtain a more…

Algebraic Topology · Mathematics 2011-01-05 C. Barwick , D. M. Kan

We consider the category of modules over sheaves of Deformation-Quantization (DQ) algebras on bionic symplectic varieties. These spaces are equipped with both an elliptic $\mathbb{G}_m$-action and a Hamiltonian $\mathbb{G}_m$-action, with…

Algebraic Geometry · Mathematics 2025-01-22 Gwyn Bellamy , Christopher Dodd , Kevin McGerty , Thomas Nevins

Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…

Algebraic Topology · Mathematics 2016-10-12 Michael A. Hill , Michael J. Hopkins

In this paper, we prove a conjecture of Blumberg and Hill regarding the existence of $N_\infty$-operads associated to given sequences $\mathcal{F} = (\mathcal{F}_n)_{n \in \mathbb{N}}$ of families of subgroups of $G\times \Sigma_n$. For…

Algebraic Topology · Mathematics 2021-09-14 Javier J. Gutiérrez , David White

We study the notion of a bifibration in simplicial sets which generalizes the classical notion of two-sided discrete fibration studied in category theory. If $A$ and $B$ are simplicial sets we equip the category of simplicial sets over…

Algebraic Topology · Mathematics 2018-07-24 Danny Stevenson

We consider the derived category of coherent sheaves on a complex vector space equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl groups of type A, B, G_2, F_4, as well as the groups…

Algebraic Geometry · Mathematics 2017-06-07 Alexander Polishchuk , Michel Van den Bergh

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 dendroidal sets is endowed with a model category structure…

Category Theory · Mathematics 2014-03-27 Denis-Charles Cisinski , Ieke Moerdijk

We introduce \emph{flagged $(\infty,n)$-categories} and prove that they are equivalent to Segal sheaves on Joyal's category ${\mathbf\Theta}_n$. As such, flagged $(\infty,n)$-categories provide a model-independent formulation of Segal…

Category Theory · Mathematics 2018-01-30 David Ayala , John Francis

In this paper we prove the equivalence of two symmetric monoidal $\infty$-categories of $\infty$-operads, the one defined in Lurie's book on Higher Algebra and the one based on dendroidal spaces. V.2 Some corrections made and exposition…

Category Theory · Mathematics 2024-10-10 Vladimir Hinich , Ieke Moerdijk

In this paper, we address the construction of homotopy bicategories of $(\infty,2)$-categories, which we take as being modeled by 2-fold Segal spaces. Our main result is the concrete construction of a functor $h_2$ from the category of…

Category Theory · Mathematics 2025-02-14 Jack Romö

In this paper, we study weakly unital dg categories as they were defined by Kontsevich and Soibelman [KS, Sect.4]. We construct a cofibrantly generated Quillen model structure on the category $\mathrm{Cat}_{\mathrm{dgwu}}(\Bbbk)$ of small…

K-Theory and Homology · Mathematics 2019-07-19 Piergiorgio Panero , Boris Shoikhet

In this paper we construct a symmetric monoidal closed model category of coherently commutative monoidal categories. The main aim of this paper is to establish a Quillen equivalence between a model category of coherently commutative…

Category Theory · Mathematics 2020-04-15 Amit Sharma

We give a gentle introduction to the concept of folding. That is, we provide an elementary discussion of equivariant categories, their weighted Grothendieck groups, and the technical aspects of computing with them. We then perform the…

Representation Theory · Mathematics 2016-04-05 Ben Elias

If all objects of a simplicial combinatorial model category \cat A are cofibrant, then there exists the homotopy model structure on the category of small functors $\sS^{\cat A}$, where the fibrant objects are homotopy functors, i.e.,…

Algebraic Topology · Mathematics 2024-07-24 Boris Chorny , David White

We characterize the exponentiable objects for a wide range of structures prevalent in $\infty$-categorical algebra, extending the construction of Day convolution to more general structures than $\infty$-operads. More precisely, we give a…

Category Theory · Mathematics 2026-04-29 Thomas Blom , Félix Loubaton , Jaco Ruit

We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In fact we give two equivalent descriptions:…

Representation Theory · Mathematics 2014-03-25 Victor Ginzburg , Simon Riche

We show that the category of categories fibred over a site is a generalized Quillen model category in which the weak equivalences are the local equivalences and the fibrant objects are the stacks, as they were defined by J. Giraud. The…

Category Theory · Mathematics 2014-04-17 Alexandru E. Stanculescu

Building upon Hovey's work on Smith ideals for monoids, we develop a homotopy theory of Smith ideals for general operads in a symmetric monoidal category. For a sufficiently nice stable monoidal model category and an operad satisfying a…

Algebraic Topology · Mathematics 2024-05-22 David White , Donald Yau

We construct a category $\OrdFor$ as an arboreal extension of $\Delta_{\mathrm{epi}}\subseteq\Delta$, whose morphisms are ordered forests composed by grafting. We define a full functor $\pi\colon \OrdFor\to\Delta_{\mathrm{epi}}^{op}$…

Algebraic Topology · Mathematics 2026-04-03 Atabey Kaygun
‹ Prev 1 3 4 5 6 7 10 Next ›