Related papers: Localization theory for triangulated categories
One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E-localisation of this model category. We study the…
We give a characterisation of those local not necessary commutative rings, for which the category of projective modules admits a triangulation with the identity as translation functor. By "admits a triangulation" we mean that the category…
The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions. In the specific setting…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
In this note, we define a recollement of additive categories, and prove that such a recollement can induce a recollement of their quotient categories. As an application, we get a recollement of quotient triangulated categories induced by…
Recently, the spectral localizer framework has emerged as an efficient approach to classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous…
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…
Visual place recognition is a fundamental capability for the localization of mobile robots. It places image retrieval in the practical context of physical agents operating in a physical world. It is an active field of research and many…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic…
The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…
In this note, I define a notion of a compactly supported object in a triangulated category. I prove a number of propositions relating this to traditional notions of support and give an application to the theory of derived Morita…
In this article, we introduce the notion of {\it concentric twin cotorsion pair} on a triangulated category. This notion contains the notions of $t$-structure, cluster tilting subcategory, co-$t$-structure and functorally finite rigid…
For a tensor triangulated category and any regular cardinal $\alpha$ we study the frame of $\alpha$-localizing tensor ideals and its associated space of points. For a well-generated category and its frame of localizing tensor ideals we…
We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke…
We study centrality of morphisms in a setting derived from that of a pointed category in which binary products commute with coequalisers. The main results of this paper show that much of the behaviour of central morphisms for unital…
Recent work has shown good recognition results in 3D object recognition using 3D convolutional networks. In this paper, we show that the object orientation plays an important role in 3D recognition. More specifically, we argue that objects…
This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main…
We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…
Robots deployed in settings such as warehouses and parking lots must cope with frequent and substantial changes when localizing in their environments. While many previous localization and mapping algorithms have explored methods of…