Related papers: Taming large categories
This work proposes a taxonomy for diagnosis computation methods which allows their standardized assessment, classification and comparison. The aim is to (i) give researchers and practitioners an impression of the diverse landscape of…
Higher Homotopy van Kampen Theorems allow the computation as colimits of certain homotopical invariants of glued spaces. One corollary is to describe homotopical excision in critical dimensions in terms of induced modules and crossed…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
We explore the structure of $\text{Fil}$, the category of filters and germs of admissible partial functions. In particular, we show that $\text{Fil}$ is a nonsymmetric closed category, as defined elsewhere by this and other authors.
Colimits are a powerful tool for the combination of objects in a category. In the context of modeling and specification, they are used in the institution-independent semantics (1) of instantiations of parameterised specifications (e.g. in…
We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm which we used to obtain first examples of so-called non-easy linear categories of…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Collaborative filtering is a rapidly advancing research area. Every year several new techniques are proposed and yet it is not clear which of the techniques work best and under what conditions. In this paper we conduct a study comparing…
We define the notion of 2-filtered 2-category and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if and only if it is a filtered category, and our…
Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
We show that the quasicategory defined as the localization of the category of (simple) graphs at the class of A-homotopy equivalences does not admit colimits. In particular, we settle in the negative the question of whether the A-homotopy…
Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…
Big Data concern large-volume, growing data sets that are complex and have multiple autonomous sources. Earlier technologies were not able to handle storage and processing of huge data thus Big Data concept comes into existence. This is a…
Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…
This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include…