A braided -category of Soergel bimodules
The Hecke algebras for all symmetric groups taken together form a braided monoidal
category that controls all quantum link invariants of type A and, by extension, the standard …
category that controls all quantum link invariants of type A and, by extension, the standard …
[PDF][PDF] A braided monoidal (∞, 2)-category of Soergel bimodules
YL Liu, A Mazel-Gee, D Reutter… - arXiv preprint arXiv …, 2024 - math.uni-bonn.de
The Hecke algebras for all symmetric groups taken together form a braided monoidal
category that controls all quantum link invariants of type A and, by extension, the standard …
category that controls all quantum link invariants of type A and, by extension, the standard …
Odd two-variable Soergel bimodules and Rouquier complexes
M Khovanov, K Putyra, P Vaz - arXiv preprint arXiv:2205.12794, 2022 - arxiv.org
We consider the odd analogue of the category of Soergel bimodules. In the odd case and
already for two variables, the transposition bimodule cannot be merged into the generating …
already for two variables, the transposition bimodule cannot be merged into the generating …
Classifying spaces for braided monoidal categories and lax diagrams of bicategories
P Carrasco, AM Cegarra, AR Garzón - Advances in Mathematics, 2011 - Elsevier
This work contributes to clarifying several relationships between certain higher categorical
structures and the homotopy type of their classifying spaces. Bicategories (in particular …
structures and the homotopy type of their classifying spaces. Bicategories (in particular …
Weak braided monoidal categories and their homotopy colimits
M Solberg - arXiv preprint arXiv:1410.6738, 2014 - arxiv.org
We show that the homotopy colimit construction for diagrams of categories with an operad
action, recently introduced by Fiedorowicz, Stelzer and Vogt, has the desired homotopy type …
action, recently introduced by Fiedorowicz, Stelzer and Vogt, has the desired homotopy type …
Categories enriched over oplax monoidal categories
T Basile, D Lejay, K Morand - arXiv preprint arXiv:2204.01032, 2022 - arxiv.org
We define a notion of category enriched over an oplax monoidal category $ V $, extending
the usual definition of category enriched over a monoidal category. Even though oplax …
the usual definition of category enriched over a monoidal category. Even though oplax …
A theorem of Retakh for exact -categories and higher extension functors
ED Børve, P Trygsland - arXiv preprint arXiv:2110.05138, 2021 - arxiv.org
We define extension $\infty $-categories for exact $\infty $-categories in terms of bifibrations.
Extension $\infty $-categories are invariant when passing to the stable hull, and …
Extension $\infty $-categories are invariant when passing to the stable hull, and …
Non-associative Categories of Octonionic Bimodules
Q Huo, G Ren - Communications in Mathematics and Statistics, 2023 - Springer
Category is put to work in the non-associative realm in the article. We focus on a typical
example of non-associative category. Its objects are octonionic bimodules, morphisms are …
example of non-associative category. Its objects are octonionic bimodules, morphisms are …
Constructing symmetric monoidal bicategories functorially
LW Hansen, M Shulman - arXiv preprint arXiv:1910.09240, 2019 - arxiv.org
We present a method of constructing monoidal, braided monoidal, and symmetric monoidal
bicategories from corresponding types of monoidal double categories that satisfy a lifting …
bicategories from corresponding types of monoidal double categories that satisfy a lifting …
Pre-rigid monoidal categories
A Ardizzoni, I Goyvaerts, C Menini - Quaestiones Mathematicae, 2023 - Taylor & Francis
Liftable pairs of adjoint functors between braided monoidal categories in the sense of [GV1]
provide auto-adjunctions between the associated categories of bialgebras. Motivated by …
provide auto-adjunctions between the associated categories of bialgebras. Motivated by …