Related papers: Elementary equivalences and accessible functors
An embedding is a function that maps entities from one algebraic structure into another while preserving certain characteristics. Embeddings are being used successfully for mapping relational data or text into vector spaces where they can…
A simple criterion for a functor to be finitary is presented: we call $F$ finitely bounded if for all objects $X$ every finitely generated subobject of $FX$ factorizes through the $F$-image of a finitely generated subobject of $X$. This is…
While most network embedding techniques model the proximity between nodes in a network, recently there has been significant interest in structural embeddings that are based on node equivalences, a notion rooted in sociology: equivalences or…
We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed…
We prove that a Lie conformal algebra L with bounded locality function is embeddable into an associative conformal algebra A with the same bound on the locality function. If L is nilpotent, then so is A, and the nilpotency index remains the…
Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across…
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
The aim of this article is to give an expository account of the equivalence between modest sets and partial equivalence relations. Our proof is entirely self-contained in that we do not assume any knowledge of categorical realizability. At…
We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…
The category $\bcalNT$ was introduced in \cite{Lobos2} in order to provide a structural setting to the study of the many Gelfand-Tsetlin subalgebras appearing in the context of the diagrammatic Soergel category of Elias and Williamson…
Word embedding models offer continuous vector representations that can capture rich contextual semantics based on their word co-occurrence patterns. While these word vectors can provide very effective features used in many NLP tasks such as…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
We systematically develop the theory of definable functors between compactly generated triangulated categories. Such functors preserve pure triangles, pure injective objects, and definable subcategories, and as such appear in a wide range…
We consider from a geometric point of view the conjectural fundamental lemma of Langlands and Shelstad for unitary groups over a local field of positive characteristic. We introduce projective algebraic varieties over the finite residue…
There are numerous studies focusing on the convergence of the principal eigenvalue $\lambda(s)$ as $s\to+\infty$ corresponding to the elliptic eigenvalue problem \begin{align*}…
The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…
A little known theorem due to Campbell is employed to establish the local embedding of a wide class of 4-dimensional spacetimes in 5-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found.…
We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better…
For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…