Related papers: On abelian 2-categories and derived 2-functors
We extend the theory of Mackey 2-functors introduced in arXiv:1808.04902 by defining the appropriate notion of rings, namely Green 2-functors. After providing the first results of our theory and abundant examples, we show how all classical…
We prove a constructive existence theorem for abelian envelopes of non-abelian monoidal categories. This establishes a new tool for the construction of tensor categories. As an example we obtain new proofs for the existence of several…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
This thesis focuses on topics in 2-category theory: in particular on double categories, pseudomonads and codescent objects. In Chapter 2 we recall all the necessary notions. In Chapter 3 we show that factorization systems can be…
We upgrade the classical operation of \textit{isomonodromic deformations} along a path $\gamma$ to a functor $\mathbb{P}_{\gamma}$ between categories of flat connections with logarithmic singularities along a divisor $D$, which itself…
We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that…
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…
(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…
We construct a representation of the string 2-group on a 2-vector space, aiming to establish it as the categorification of the spinor representation. Our model for 2-vector spaces is based on the Morita bicategory of von Neumann algebras,…
We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is…
In arXiv:2011.03313, the author has constructed a category of abstractly automorphic representations for $\mathrm{GL}(2)$ over a function field $F$. This is a symmetric monoidal Abelian category, constructed with the goal of having the…
We collect some isomorphisms of categories and bijections of structures using the Kleisli and Eilenberg-Moore 2-adjunctions.
We summarize our recent work [1-3] concerning the formulation of two-particle-irreducible (2PI) functional techniques for abelian gauge field theories.
In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. Our goal is to create a path towards a general theory of…
In the efforts to define a 2-categorical analog of an abelian category, two (or three) notions of "abelian 2-categories" are defined. One is the relatively exact 2-category, and the other(s) is the (2-)abelian Gpd-category. We compare these…
This paper is a sequel to "T-structures and twisted complexes on derived injectives" by the same author with W. Lowen and M. Van den Bergh. We define a dg-category of unbounded twisted complexes on a dg-category, which is particularly…
We develop Morita theory of monoids in a closed symmetric monoidal category, in the context of enriched category theory.
The notion of a weak duality involution on a bicategory was recently introduced by Shulman in [arXiv:1606.05058]. We construct a weak duality involution on the fully dualisable part of $\text{Alg}$, the Morita bicategory of…
This paper is a fundamental study of the Real $2$-representation theory of $2$-groups. It also contains many new results in the ordinary (non-Real) case. Our framework relies on a $2$-equivariant Morita bicategory, where a novel…
We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the $G$-comodules…