Related papers: Higher Frobenius-Schur Indicators for Pivotal Cate…
We introduce lifespan functors, which are endofunctors on the category of persistence modules that filter out intervals from barcodes according to their boundedness properties. They can be used to classify injective and projective objects…
We describe the classification of ranked definably quasi-Frobenius groups of odd type : dihedral configurations are isomorphic to PGL(2, K) for K an algebraically closed field of characteristic other than two; Frobenius groups are spilt and…
We generalise to a group homomorphism $\tau$ the $\chi$-graded categories of S\"{o}zer and Virelizier. These are categories in which both morphisms and objects have compatible degrees. We give a 'half-enriched' Yoneda lemma, a structure…
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categories as algebraic structures in $\mathbf{Prof}$, the monoidal…
The study of abstraction and composition - the focus of category theory - naturally leads to sophisticated diagrams which can encode complex algebraic semantics. Consequently, these diagrams facilitate a clearer visual comprehension of…
We define "sliding functors", which are exact endofunctors of the category of multi-graded modules over a polynomial ring. They preserve several invariants of modules, especially the (usual) depth and Stanley depth. In a similar way, we can…
For a toric Deligne-Mumford (DM) stack, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism on a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the…
The aim of this work is to offer a family of invariants that allows us to classify finite potent endomorphisms on arbitrary vector spaces, generalizing the classification of endomorphisms on finite-dimensional vector spaces. As a particular…
We call a tensor functor $F:\mathcal{C}\to\mathcal{D}$ between finite tensor categories $\otimes$-Frobenius if its left and right adjoints are isomorphic as $\mathcal{C}$-bimodule functors. We give several characterizations of this notion…
We study the categorical notion of braid gauging and obtain its classical Hopf algebraic description. We demonstrate how braid gauging can provide new insights on certain categorical invariants, such as the fusion rules and the higher…
This article studies the categorical setting of Abramsky, Haghverdi, and Scott's untyped linear combinatory algebras, and relates this to more recent work of Abramsky and Heunen on Frobenius algebras in the infinitary setting. The key to…
We formulate two new $\mathbb Z[q,q^{-1}]$-linear diagrammatic monoidal categories, the affine $q$-web category and the affine $q$-Schur category, as well as their respective cyclotomic quotient categories. Diagrammatic integral bases for…
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical…
We study generalizations of Schur functors from categories consisting of flags of vector spaces. We give different descriptions of the category of such functors in terms of representations of certain combinatorial categories and infinite…
We study monoidal categories that enjoy a certain weakening of the rigidity property, namely, the existence of a dualizing object in the sense of Grothendieck and Verdier. We call them Grothendieck-Verdier categories. Notable examples…
It is well-known that the value of the Frobenius-Schur indicator $|G|^{-1} \sum_{g\in G} \chi(g^2)=\pm1$ of a real irreducible representation of a finite group $G$ determines which of the two types of real representations it belongs to,…
Let $R$ be a commutative ring with unit. We develop a Hochschild cohomology theory in the category $\mathcal{F}$ of linear functors defined from an essentially small symmetric monoidal category enriched in $R$-Mod, to $R$-Mod. The category…
We develop a theory of Frobenius functors for symmetric tensor categories (STC) $\mathcal{C}$ over a field $\bf k$ of characteristic $p$, and give its applications to classification of such categories. Namely, we define a twisted-linear…
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categories as algebraic structures in Prof, the monoidal bicategory…
We show that the Frobenius and Verschiebung maps that are fundamental to Witt vectors lift to the reduced K-theory of endomorphisms. In particular, we define Frobenius and Verschiebung maps for the reduced K-theory of twisted endomorphisms…