27 citations · 71 across the 31 of their papers we have counts for
32 papers
Monoidal adjunctions and abelian envelopes
Johannes Flake, Robert Laugwitz, Sebastian Posur
We show how monoidal adjunctions can be used to prove the existence of monoidal abelian envelopes of pseudo-tensor categories, in particular, those admitting a combinatorial descri…
Fully exact and fully dualizable module categories
Azat M. Gainutdinov, Robert Laugwitz
We define fully exact module categories, a subclass of exact module categories over a finite braided tensor category that is stable under the relative Deligne product. In contrast,…
Temperley-Lieb categories with coloured regions and Jones-Wenzl projectors
Cameron Howat, Robert Laugwitz, Martin Ray
Generalised Temperley-Lieb categories with regions labelled by elements of a commutative algebra were introduced by M. Khovanov and the second author in [Pure Appl. Math. Q. 19 (20…
Presentations for small reflection equation algebras of type A
Juliet Cooke, Robert Laugwitz
We give presentations, in terms of the generators and relations, for the reflection equation algebras of type and , i.e., the covariantized algebras of the dual Hopf a…
Frobenius monoidal functors induced by Frobenius extensions of Hopf algebras
Johannes Flake, Robert Laugwitz, Sebastian Posur
We show that induction along a Frobenius extension of Hopf algebras is a Frobenius monoidal functor in great generality, in particular, for all finite-dimensional and all pointed H…
Shifted Poisson structures on higher Chevalley-Eilenberg algebras
Cameron Kemp, Robert Laugwitz, Alexander Schenkel
This paper develops a graphical calculus to determine the -shifted Poisson structures on finitely generated semi-free commutative differential graded algebras. When applied to t…
Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers
Johannes Flake, Robert Laugwitz, Sebastian Posur
We identify general conditions, formulated using the projection formula morphisms, for a functor that is simultaneously left and right adjoint to a strong monoidal functor to be a…
Infinitesimal 2-braidings from 2-shifted Poisson structures
Cameron Kemp, Robert Laugwitz, Alexander Schenkel
It is shown that every -shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra defines a very explicit infinitesimal -braidin…
Projection formulas and induced functors on centers of monoidal categories
Johannes Flake, Robert Laugwitz, Sebastian Posur
Given a monoidal adjunction, we show that the right adjoint induces a braided lax monoidal functor between the corresponding Drinfeld centers provided that certain natural transfor…
The Braids on your Blanket
Michelle Cheng, Robert Laugwitz
In this expositional essay, we introduce some elements of the study of groups by analysing the braid pattern on a knitted blanket. We determine that the blanket features pure braid…
Reflective centers of module categories and quantum K-matrices
Robert Laugwitz, Chelsea Walton, Milen Yakimov
Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category and $\mathca…
Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras
Samuel Hannah, Robert Laugwitz, Ana Ros Camacho
We construct a separable Frobenius monoidal functor from to for any subgroup of which…
Finite-dimensional quantum groups of type Super A and non-semisimple modular categories
Robert Laugwitz, Guillermo Sanmarco
We construct a series of finite-dimensional quantum groups as braided Drinfeld doubles of Nichols algebras of type Super A, for an even root of unity, and classify ribbon structure…
Differential graded cell 2-representations
Robert Laugwitz, Vanessa Miemietz
This article develops a theory of cell combinatorics and cell 2-representations for differential graded 2-categories. We introduce two types of partial preorders, called the strong…
Pretriangulated 2-representations via dg algebra 1-morphisms
Robert Laugwitz, Vanessa Miemietz
This paper develops a theory of pretriangulated 2-representations of dg 2-categories. We characterize cyclic pretriangulated 2-representations, under certain compactness assumption…
Constructing non-semisimple modular categories with local modules
Robert Laugwitz, Chelsea Walton
We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previo…
Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories
Johannes Flake, Robert Laugwitz, Sebastian Posur
Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. Th…
The indecomposable objects in the center of Deligne's category
Johannes Flake, Nate Harman, Robert Laugwitz
We classify the indecomposable objects in the monoidal center of Deligne's interpolation category by viewing as a model-theoretic limit in rank and characteri…
Planar diagrammatics of self-adjoint functors and recognizable tree series
Mikhail Khovanov, Robert Laugwitz
A pair of biadjoint functors between two categories produces a collection of elements in the centers of these categories, one for each isotopy class of nested circles in the plane.…
Constructing non-semisimple modular categories with relative monoidal centers
Robert Laugwitz, Chelsea Walton
This paper is a contribution to the construction of non-semisimple modular categories. We establish when Müger centralizers inside non-semisimple modular categories are also modula…
Braided commutative algebras over quantized enveloping algebras
Robert Laugwitz, Chelsea Walton
We produce braided commutative algebras in braided monoidal categories by generalizing Davydov's full center construction of commutative algebras in centers of monoidal categories.…
On the Monoidal Center of Deligne's Category Rep(S_t)
Johannes Flake, Robert Laugwitz
We explicitly compute a monoidal subcategory of the monoidal center of Deligne's interpolation category Rep(S_t), for t not necessarily a natural number, and we show that this subc…
Noncommutative Shifted Symmetric Functions
Robert Laugwitz, Vladimir Retakh
We introduce a ring of noncommutative shifted symmetric functions based on an integer-indexed sequence of shift parameters. Using generating series and quasideterminants, this mult…
A categorification of cyclotomic rings
Robert Laugwitz, You Qi
For any natural number , we construct a triangulated monoidal category whose Grothendieck ring is isomorphic to the ring of cyclotomic integers .