Related papers: On the monoidality of Saito reflection functors

Given a not necessarily semisimple modular tensor category C, we use the corresponding 3d TFT defined in [arXiv:1912.02063] to explicitly describe a modular functor as a symmetric monoidal 2-functor from a 2-category of oriented bordisms to…

For a symplectic geometry $X$, suppose the (derived) Fukaya category $\mathrm{Fuk}(X)$ of $X$ is equipped with a monoidal structure. Then its Balmer spectrum recovers a mirror $Y$ of $X$ if there exists homological mirror symmetry…

In this short note we study Lie algebras in the framework of symmetric monoidal categories. After a brief review of the existing work in this field and a presentation of earlier studied and new examples, we examine which functors preserve…

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice),…

In this paper, we determine derivations of Borel subalgebras and their derived subalgebras called nilradicals, in Kac-Moody algebras (and contragredient Lie algebras) over any field of characteristic 0; and we also determine automorphisms…

We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal…

We realize the enveloping algebra of the positive part of a symmetrizable Kac-Moody algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-Gorenstein algebras of dimension 1.

We apply the notion of relative adjoint functor to generalise closed monoidal categories. We define representations in such categories and give their relation with left actions of monoids. The translation of these representations under lax…

We generalize the notion of a Kac-Moody Lie algebra to the setting of Deligne Categories. Then we derive the Kac-Weyl formula for the category $\mathcal{O}$ integrable representations for such an algebra. This paper generalizes results of…

For any algebra morphism in a monoidal category, we provide sufficient conditions (which are also necessary if the unit is a left tensor generator) for the attached induction functor being semiseparable. Under mild assumptions, we prove…

Using the category of finite sets and injections, we construct a new model for the multilinearization of multifunctors between spaces that appears in the derivatives of Goodwillie calculus. We show that this model yields a lax monoidal…

We verify that a certain functor $D\colon\text{Sp}^\Sigma(\text{Ch}^+)\to\text{Ch}$ is symmetric monoidal. This functor is used elsewhere in developing the model category theory of symmetric spectra and of chain complexes graded over…

We use mixed Hodge theory to show that the functor of singular chains with rational coefficients is formal as a lax symmetric monoidal functor, when restricted to complex schemes whose weight filtration in cohomology satisfies a certain…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

A strongly reflective modular form with respect to an orthogonal group of signature (2,n) determines a Lorentzian Kac--Moody algebra. We find a new geometric application of such modular forms: we prove that if the weight is larger than n…

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 transformations, called projection formula morphisms, are…

We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild…

We develop and extend the theory of Mackey functors as an application of enriched category theory. We define Mackey functors on a lextensive category $\E$ and investigate the properties of the category of Mackey functors on $\E$. We show…

We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a…

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be…