Related papers: Nakayama categories and groupoid quantization
Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exact…
For a finite group $D$, we study categorical factorisation homology on oriented surfaces equipped with principal $D$-bundles, which `integrates' a (linear) balanced braided category $\mathcal{A}$ with $D$-action over those surfaces. For…
In this paper we study the class of \emph{split Nakamura manifolds}, which are a type of solvmanifolds generalizing Nakamura's threefold, defined as quotients of the semidirect product $\mathbb{C}^n \rtimes_\rho \mathbb{C}$ by a lattice. We…
We review basic properties of the Nakayama functor for coalgebras and introduce a number of applications to tensor categories. We also give equivalent conditions for a coquasi-bialgebra with preantipode to admit a non-zero cointegral.
We extend to the category of relative regular holonomic modules on a manifold $X$, parametrized by a curve $S$, the Hermitian duality functor (or conjugation functor) of Kashiwara. We prove that this functor is an equivalence with the…
Given a smooth 3-fold $Y$, a line bundle $L \to Y$, and a section $s$ of $L$ such that the vanishing locus of $s$ is a normal crossings surface $X$ with graph-like singular locus, we present a way to reconstruct the singularity category of…
The group scheme of universal centralizers of a complex reductive group $G$ has a quantization called the spherical nil-DAHA. The category of modules over this ring is equivalent, as a symmetric monoidal category, to the category of…
In this paper, we define indexed type theories which are related to indexed ($\infty$-)categories in the same way as (homotopy) type theories are related to ($\infty$-)categories. We define several standard constructions for such theories…
Jasso-K\"{u}lshammer introduced the class of $d$-Nakayama algebras as a higher dimensional analogue of Nakayama algebras. In particular, they are endowed with a distinguished $d\mathbb{Z}$-cluster tilting subcategory. In this paper, we…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
Sati and Schreiber [arXiv:2402.18473, arXiv:2512.12431] have proposed that charge quantisation in quantum field theory and string theory is governed by a homotopy type $\mathcal A$. We provide a refinement of this postulate, incorporating…
This is intended as a self-contained introduction to the representation theory developed in order to create a Poincare 2-category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation…
We introduce continuous analogues of Nakayama algebras. In particular, we introduce the notion of (pre-)Kupisch functions, which play a role as Kupisch series of Nakayama algebras, and view continuous Nakayama representations as a special…
We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this…
The stable module category has been realized as a subcategory of the unbounded homotopy category of projective modules by Kato. We construct the triangulated hull of this subcategory inside the homotopy category. This can also be used to…
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
To any rigid analytic space (in the sense of Fujiwara-Kato) we assign an $\mathbb{A}^1$-invariant rigid analytic homotopy category with coefficients in any presentable category. We show some functorial properties of this assignment as a…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
We provide a fairly self-contained account of the localisation and cofinality theorems for the algebraic $\mathrm{K}$-theory of stable $\infty$-categories. It is based on a general formula for the evaluation of an additive functor on a…
We systematically study the commutative factorization categories over the Ran space. We fill in what we consider as a gap in the construction of the factorizable Satake functor in the constructible setting in arXiv:1708.07205,…