Related papers: Deligne-Knop tensor categories and functoriality

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 subcategory is a ribbon category. For t=n, a natural number,…

We derive several tools for classifying tensor ideals in monoidal categories. We use these results to classify tensor ideals in Deligne's universal categories RepO, RepGL and RepP. These results are then used to obtain new insight into the…

We show that each rigid monoidal category A over a field defines a family of universal tensor categories, which together classify all faithful monoidal functors from A to tensor categories. Each of the universal tensor categories classifies…

In our recent paper [Sh1] a version of the "generalized Deligne conjecture" for abelian $n$-fold monoidal categories is proven. For $n=1$ this result says that, given an abelian monoidal $k$-linear category $\mathscr{A}$ with unit $e$, $k$…

For any good tilting module $T$ over a ring $A$, there exists an $n$-symmetric subcategory $\mathscr{E}$ of a module category such that the derived category of the endomorphism ring of $T$ is a recollement of the derived categories of…

In a previous work by the author it was shown that every finite dimensional algebraic structure over an algebraically closed field of characteristic zero K gives rise to a character $K[X]_{aug}\to K$, where $K[X]_aug$ is a commutative Hopf…

We endow the homotopy category of well generated (pretriangulated) dg categories with a tensor product satisfying a universal property. The resulting monoidal structure is symmetric and closed with respect to the cocontinuous RHom of dg…

Let $W$ be a finite dimensional algebraic structure (e.g. an algebra) over a field $K$ of characteristic zero. We study forms of $W$ by using Deligne's Theory of symmetric monoidal categories. We construct a category $\mathcal{C}_W$, which…

Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne's category admits a unique nontrivial family of modified trace functions. Such modified trace…

In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such equivalences can be used to…

The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic categories and their operads. This theory is, in our opinion, of an independent value. In Part 2 we use this new theory together with our previous…

It has long been known that every weak monoidal category A is equivalent via monoidal functors and monoidal natural transformations to a strict monoidal category st(A). We generalise the definition of weak monoidal category to give a…

The category of strict polynomial functors inherits an internal tensor product from the category of divided powers. To investigate this monoidal structure, we consider the category of representations of the symmetric group which admits a…

The main objective of the present paper is to present a version of the Tannaka-Krein type reconstruction Theorems: If $F:B\to C$ is an exact faithful monoidal functor of tensor categories, one would like to realize $B$ as category of…

In the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-classes of such internal relations are first described in terms…

This is mostly an overview. Given finitely presentable abelian categories $A$ and $B$, we sketch the construction of an abelian category of continuous functors from $A$ to $B$ that has nice $2$-categorical behaviour and gives an explicit…

The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter t while producing categories of representations of the symmetric group when modded out…

Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…

We extend Deligne's notion of determinant functor to tensor triangulated categories. Specifically, to account for the multiexact structure of the tensor, we define a determinant functor on the 2-multicategory of triangulated categories and…

Given a category $\mathcal{E}$, we establish sufficient conditions on a faithful isofibration $\mathcal{E}\rightarrow\operatorname{Mon}(\mathcal{V})$ valued in the category of monoids internal to a monoidal additive category $\mathcal{V}$…