Related papers: Barr's Embedding Theorem for Enriched Categories

Binomial Theorem for (N+n)^r is described with non-commuting variables N and n.

We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.

Contextualized embeddings vary by context, even for the same token, and form a distribution in the embedding space. To analyze this distribution, we focus on the norm of the mean embedding and the variance of the embeddings. In this study,…

We evaluate chemical patent word embeddings against known biomedical embeddings and show that they outperform the latter extrinsically and intrinsically. We also show that using contextualized embeddings can induce predictive models of…

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…

Using Carleson measure theorem of weighted Bergman spaces, we provide a complete characterization of embedding theorem for Dirichlet type spaces. As an application, we study the Volterra integral operator and multipliers for Dirichlet type…

We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…

We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided $G$-crossed categories.

We introduce a general notion of enrichment for homotopy-coherent algebraic structures described by Segal conditions, using the framework of "algebraic patterns" developed in our previous work. This recovers several known examples of…

A representation embedding between cartesian theories can be defined to be a functor between respective categories of models that preserves finitely-generated projective models and that preserves and reflects certain epimorphisms. This…

It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal…

Let $b$, $b'$ be commutative monoids in a B\'{e}nabou cosmos. Motivated by six-functor formalisms in algebraic geometry, we prove that the category of commutative monoids over $b\otimes b'$ is equivalent to the category of cocontinuous lax…

We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivalences are Dwyer-Kan equivalences, i.e. enriched functors…

This paper have two parts. In the first part we discuss word embeddings. We discuss the need for them, some of the methods to create them, and some of their interesting properties. We also compare them to image embeddings and see how word…

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.

We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.

We prove that every $1$-error-correcting code over a finite field can be embedded in a $1$-perfect code of some larger length. Embedding in this context means that the original code is a subcode of the resulting $1$-perfect code and can be…

Given a category $\mathcal C$ and a directed partially ordered set $J$, a certain category $pro^J -\mathcal C$ on inverse systems in $\mathcal C$ is constructed such that the ordinary pro-category $pro-\mathcal C$ is the most special case…

We investigate the problem of inducing word embeddings that are tailored for a particular bilexical relation. Our learning algorithm takes an existing lexical vector space and compresses it such that the resulting word embeddings are good…

We prove an extension of the Regularity Lemma with vertex and edge weights which can be applied for a large class of graphs. The applications involve random graphs and a weighted version of the Erd\H{o}s-Stone theorem. We also provide means…