Related papers: Filtered colimit elimination from Birkhoff's varie…

This is a survey and research note on the modified Orlik conjecture derived from the division theorem introduced in [2]. The division theorem is a generalization of classical addition-deletion theorems for free arrangements. The division…

We prove fibration theorems \`a la Milnor for differentiable real maps with non isolated critical values. We study the situation for maps with linear discriminant, and prove that the concept of d-regularity is the key point for the…

Let $Z$ be an affine algebraic variety and $X$ be a smooth flexible variety. We develop some criteria under which $Z$ admits a closed embedding into $X$. In particular, we show that if $X$ is isomorphic (as an algebraic variety) to a…

We consider the following practical question: given a finite algebra A in a finite language, can we efficiently decide whether the variety generated by A has a difference term? We answer this question (positively) in the idempotent case and…

Motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one - intuitively, the topological analogue of a Kripke polynomial functor. Among other…

To every finite-dimensional $\mathbb C$-algebra $\Lambda$ of finite representation type we associate an affine variety. These varieties are a large generalization of the varieties defined by "$u$ variables" satisfying "$u$-equations", first…

We show that in a category with pullbacks, arbitrary sifted colimits may be constructed as filtered colimits of reflexive coequalizers. This implies that "lex sifted colimits", in the sense of Garner--Lack, decompose as Barr-exactness plus…

We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…

Determining when a finite dimensional algebra satisfies the finiteness property known as the $(\textbf{Fg})$-condition is of fundamental importance in the celebrated and influential theory of support varieties. We give an answer to this…

It is known that Plotkin's reduction theorem is very important for his theory of universal algebraic geometry [arXiv:math. GM/0210187], [arXiv:math. GM/0210194]. It turns out that this theorem can be generalized to arbitrary categories…

We give a general version of Bryc's theorem valid on any topological space and with any algebra $\mathcal{A}$ of real-valued continuous functions separating the points, or any well-separating class. In absence of exponential tightness, and…

The well-known Leibniz theorem (Leibniz Criterion or alternating series test) of convergence of alternating series is generalized for the case when the absolute value of terms of series are "not absolutely monotonously" convergent to zero.…

For all sufficiently large odd integers $n$, the following version of Higman's embedding theorem is proved in the variety ${\cal B}_n$ of all groups satisfying the identity $x^n=1$. A finitely generated group $G$ from ${\cal B}_n$ has a…

We show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thus improving the existing Cayley/Holland-style embedding theorem. We use this to show that the variety of all…

In this paper, we show that a partitioned formula \phi is dependent if and only if \phi has uniform definability of types over finite partial order indiscernibles. This generalizes our result from a previous paper [1]. We show this by…

We prove a version of the Poincar\'e-Birkhoff-Witt Theorem for profinite pronilpotent Lie algebras in which their symmetric and universal enveloping algebras are replaced with appropriate formal analogues and discuss some immediate…

We study a family of affine varieties arising from a version of an old problem due to Birkhoff asking for the classification of embeddings of finite abelian p-groups. We show that all of these varieties are irreducible and have a dense…

In this paper we prove an $\infty$-categorical version of the reflection theorem of Ad\'amek-Rosick\'y. Namely, that a full subcategory of a presentable $\infty$-category which is closed under limits and $\kappa$-filtered colimits is a…

When given a class of functions and a finite collection of sets, one might be interested whether the class in question contains any function whose domain is a subset of the union of the sets of the given collection and whose restrictions to…

This article concerns the Herrlich-Chew theorem stating that a Hausdorff zero-dimensional space is $\mathbb{N}$-compact if and only if every clopen ultrafilter with the countable intersection property in this space is fixed. It also…