Related papers: Limit Models in Metric Abstract Elementary Classes…

Properties of categories enriched over the category of metric spaces are investigated and applied to a study of constructions known from that category and the category of Banach spaces. For every class of morphisms satisfying a mild…

We review generalized additive models as a type of ``transparent'' model that has recently seen renewed interest in the deep learning community as neural additive models. We highlight multiple types of nonidentifiability in this model class…

We study the spectrum of limit models assuming the existence of a nicely behaved independence notion. Under reasonable assumptions, we show that all `long' limit models are isomorphic, and all `short' limit models are non-isomorphic.…

We to a large extent sort out when does a (first order complete theory) T have a superlimit model in a cardinal lambda . Also we deal with relation notions of being limit.

This the first of a series of articles dealing with abstract classification theory. The apparatus to assign systems of cardinal invariants to models of a first order theory (or determine its impossibility) is developed in [Sh:a]. It is…

We describe the framework for the notion of a restricted inverse limit of categories, with the main motivating example being the category of polynomial representations of the group $GL_{\infty}$. This category is also known as the category…

We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense…

We give describe several models for $(\infty,n)$-categories, with an emphasis on models given by diagrams of sets and simplicial sets. We look most closely at the cases when $n \leq 2$, then summarize methods of generalizing for all $n$.

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…

These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.

This study explores the impact of class outliers on the effectiveness of example-based explainability methods for black-box machine learning models. We reformulate existing explainability evaluation metrics, such as correctness and…

We explain how categories, and groupoids, can be seen as models for a Lawvere ${\mathfrak Gr}$-theory, where ${\mathfrak Gr}$ is the category of graphs, and show that for Lawvere ${\mathfrak Gr}$-theories finitely presentable models are…

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

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…

Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…

We consider epimorphisms and several variant notions -- split, effective, regular, strong, and extremal -- and determine which of these coincide in the metric coarse and coarsely Lipschitz categories. In particular, we characterise extremal…

In this paper we characterize those accessible $\mathcal V$-categories that have limits of a specified class. We do this by introducing the notion of companion $\mathfrak C$ for a class of weights $\Psi$, as a collection of special types of…

Our goal is to develop a limit approach for a class of problems in additive combinatorics that is analogous to the limit theory of dense graph sequences. We introduce metric, convergence and limit objects for functions on groups and for…

Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems of metrics in a same conformal class that fixes the boundary and satisfy certain integral conditions on the the scalar curvatures and the mean…

Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in general, they can only be stated for regular categories. We…