Related papers: What is an equivalence in a higher category?
We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections.
We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.
Part of the theoretical motivation for improving the present level of testing of the equivalence principle is reviewed. The general rationale for optimizing the choice of pairs of materials to be tested is presented. One introduces a…
The concept of n-categories and related subject is considered. An n-category is described as an n-graph with a composition. A new definition of operad is presented. Some illustrative examples are given.
The objective of this paper is to provide a fairly general model category context in which one can perform Goodwille Calculus. There are two main parts to the paper, the first establishing general conditions which guarantee the existence of…
Synonymy and translational equivalence are the relations of sameness of meaning within and across languages. As the principal relations in wordnets and multi-wordnets, they are vital to computational lexical semantics, yet the field suffers…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
This study is to review the approaches used for measuring sentences similarity. Measuring similarity between natural language sentences is a crucial task for many Natural Language Processing applications such as text classification,…
In this paper we complete a chain of explicit Quillen equivalences between the model category for $\Theta_{n+1}$-spaces and the model category of small categories enriched in $\Theta_n$-spaces. The Quillen equivalences given here connect…
Many categories have been used to model concurrency. Using any of these, the challenge is to reduce a given model to a smaller representation which nevertheless preserves the relevant computer-scientific information. That is, one wants to…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
An elementary theory of strict $\infty $-categories with application to concrete duality is given. New examples of first and second order concrete duality are presented.
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…
Secure computation of equivalence has fundamental application in many different areas, including healthcare. We study this problem in the context of matching an individual identity to link medical records across systems. We develop an…
We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
This is a survey article on selected topics in approximation theory. The topics either use techniques from the theory of several complex variables or arise in the study of the subject. The survey is aimed at readers having an acquaintance…
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.