Related papers: What is an equivalence in a higher category?

We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…

In this paper, we define indexed type theories which are related to indexed ($\infty$-)categories in the same way as (homotopy) type theories are related to ($\infty$-)categories. We define several standard constructions for such theories…

The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…

Similarity functions measure how comparable pairs of elements are, and play a key role in a wide variety of applications, e.g., notions of Individual Fairness abiding by the seminal paradigm of Dwork et al., as well as Clustering problems.…

We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…

We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplicial category of filters; this is, moreover, implicit in the…

This is a companion overview paper to arXiv:2409.17489: we give all the main definitions, constructions and statements, but no proofs.

We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories.

We give a detailed overview over known results for (no-)collision of a body with the boundary of its container.

The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.

Usually one compares the accuracy of two competing classifiers via null hypothesis significance tests (nhst). Yet the nhst tests suffer from important shortcomings, which can be overcome by switching to Bayesian hypothesis testing. We…

A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and…

This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck…

We define the notion of 1-affineness for a prestack, and prove an array of results that establish 1-affineness of certain types of prestacks.

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…

In this paper we put a cofibrantly generated model category structure on the category of small simplicial categories. The weak equivalences are a simplicial analogue of the notion of equivalence of categories.

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…

In light of Phillips' contention regarding the impracticality of Search Neutrality, asserting that non-epistemic factors presently dictate result prioritization, our objective in this study is to confront this constraint by questioning…

Consensus clustering fuses diverse basic partitions (i.e., clustering results obtained from conventional clustering methods) into an integrated one, which has attracted increasing attention in both academic and industrial areas due to its…

Quantification is the machine learning task of estimating test-data class proportions that are not necessarily similar to those in training. Apart from its intrinsic value as an aggregate statistic, quantification output can also be used to…