相关论文: A Problem in Categories

The problem of deciding, given a complex variety X, a point x in X, and a subvariety Z of X, whether there is an automorphism of X mapping x into Z is proved undecidable. Along the way, we prove the undecidability of a version of Hilbert's…

Two natural decision problems regarding the XML query language XQuery are well-definedness and semantic type-checking. We study these problems in the setting of a relational fragment of XQuery. We show that well-definedness and semantic…

The central focus is on clarifying the distinction between sets and proper classes. To this end we identify several categories of concepts (surveyable, definite, indefinite), and we attribute the classical set theoretic paradoxes to a…

For any set $X$, ${\mathcal P}(X)$ denotes the collection of all subsets of $X$, ordered by inclusion. A {\it cutset} in ${\mathcal P}(X)$ is a subset of ${\mathcal P}(X)$ which meets every maximal chain of ${\mathcal P}(X)$. A cutset is…

A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along…

Inverse limits, unlike direct limits, can in general be void, [1]. The existence of fixed points for arbitrary mappings $T : X \longrightarrow X$ is conjectured to be equivalent with the fact that related direct limits of all finite…

A classic problem in analysis is to solve nonlinear equations of the form \begin{equation*} F(x)=0, \end{equation*} where $F:D^n\to \mathbb{R}^m$ is a continuous map of the closed unit disk $D^n\subset\mathbb{R}^n$ in $\mathbb{R}^m$. A…

We construct certain non-degenerate maps and sets, mainly in the complex-analytic category. For example, we show that for every countable subset S in an irreducible complex space X there exists a holomorphic map from the unit disk to X such…

Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C.…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs

We determine the conditions for the existence or not of cycles for several families of generalized 3x + 1 mappings and develop a method to find them.

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…

Let $X$ be a set, $B_{X}$ denotes the family of all subsets of $X$ and $F: X \longrightarrow B_{X}$ be a set-valued mapping such that $x \in F(x)$, $sup_{x\in X} | F(x)|< \kappa$, $sup_{x\in X} | F^{-1}(x)|< \kappa$ for all $x\in X$ and…

The problem of classifying all unitary R-matrices of arbitrary finite dimension that have precisely two distinct eigenvalues is described, working up to a natural equivalence relation given by the characters of their braid group…

A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…

The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all "good" explanations of categories so far have been designed by mathematicians, or at least theoreticians with a strong…

Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the…

Let $X$ be a surface, possibly with boundary. Suppose it has infinite genus or infinitely many punctures, or a closed subset which is a disk with a Cantor set removed from its interior. For example, $X$ could be any surface of infinite type…

In this paper, the Identity Problem for certain groups, which asks if the subsemigroup generated by a given finite set of elements contains the identity element, is related to problems regarding ordered groups. Notably, the Identity Problem…