Related papers: Morita equivalence methods in classification of fu…
The classification of phases using categorical symmetries has greatly expanded the landscape of gapped and gapless phases. So far, however, these developments have largely been restricted to phases with unitary (higher-)categorical…
This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. Within the framework of Lie groupoids equipped with a…
We describe the structure of a generalized near-group fusion category and present an example of this class of fusion categories which arises from the extension of a Fibonacci category. We then classify slightly degenerate generalized…
In this paper we construct two new fusion categories and many new subfactors related to the exceptional Extended Haagerup subfactor. The Extended Haagerup subfactor has two even parts EH1 and EH2. These fusion categories are mysterious and…
Categorical aspects of the theory of modules over trusses are studied. Tensor product of modules over trusses is defined and its existence established. In particular, it is shown that bimodules over trusses form a monoidal category. Truss…
We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the base field has an odd characteristic. This assumption on the characteristic is for…
A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara-Yamagami categories and the even sectors of the E6 and affine-D5 subfactors, though there are…
Fusion is a common tool for the analysis and utilization of available datasets and so an essential part of data mining and machine learning processes. However, a clear definition of the type of fusion is not always provided due to…
We consider the localisation of the 2-category of diffeological groupoids at weak equivalences from the perspective of anafunctors, and with this language, prove that the localisation of the 2-category of Lie groupoids is an essentially…
This is a survey paper, based on lectures given at the Workshop on "Structured ring spectra and their applications" which took place January 21-25, 2002, at the University of Glasgow. The term `Morita theory' is usually used for results…
The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module category are given by internal Homs and coHoms, respectively. We…
We introduce the notion of a quasi-Frobenius algebra in a finite tensor category $\mathcal{C}$ and give equivalent conditions for an algebra in $\mathcal{C}$ to be quasi-Frobenius. A quasi-Frobenius algebra in $\mathcal{C}$ is not…
We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…
We prove two results from Morita theory of stable model categories. Both can be regarded as topological versions of recent algebraic theorems. One is on recollements of triangulated categories, which have been studied in the algebraic case…
We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Fr\"olicher, Sikorski, Smith, and Souriau. The method of comparison is to construct functors between the categories that…
In this article, we apply the derived Morita theory of dg-categories to show how to extend the domain of validity of many identities relating Morita invariants from associative dg-algebras toward non-commutative scheme. Doing so, we obtain…
In arXiv:2211.04917, it was shown that, over an algebraically closed field of characteristic zero, every fusion 2-category is Morita equivalent to a connected fusion 2-category, that is, one arising from a braided fusion 1-category. This…
We propose the notion of quasi-abelian third cohomology of crossed modules, generalizing Eilenberg and MacLane's abelian cohomology and Ospel's quasi-abelian cohomology, and classify crossed pointed categories in terms of it. We apply the…
We review Morita equivalence for finite type $k$-algebras $A$ and also a weakening of Morita equivalence which we call stratified equivalence. The spectrum of $A$ is the set of equivalence classes of irreducible $A$-modules. For any finite…
We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. This category is shown to admit a compact generator which is given by the stabilization of the residue field. We deduce a…