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Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
For a completely regular space $X$, denote by $C_p(X)$ the space of continuous real-valued functions on $X$, with the pointwise convergence topology. In this article we strengthen a theorem of O. Okunev concerning preservation of some…
Given a relatively projective birational morphism $f\colon X\to Y$ of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over $Y$) generators $T_{X,f}$ and $S_{X,f}$ in $\mathcal{D}^b(X)$. We…
We show that if $C_p(X\times Z)$ is homeomorphic to $C_p(Y\times Z)$, where $Z$ is compact, and $X$ and $Y$ are of countable netweight, then $C_p(X\times M)$ is homeomorphic to $C_p(Y\times M)$ for some metric compactum $M$.
Let C denote any of the following cardinal characteristics of Boolean algebras: incomparability, spread, character, pi-character, hereditary Lindelof number, hereditary density. It is shown to be consistent that there exists a sequence…
Every small category $C$ has a classifying space $BC$ associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper we…
By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…
Some boundedness properties of function spaces (considered as topological groups) are studied.
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…
This is a major update of the previous version. The methods of the paper are now fully constructive and the style is "formalization ready" with the emphasis on the possibility of formalization both in type theory and in constructive set…
A general discussion of the conformal Ward identities is presented in the context of logarithmic conformal field theory with conformal Jordan cells of rank two. The logarithmic fields are taken to be quasi-primary. No simplifying…
The paper examines machines of the type of the $\Gamma$-spaces of Segal which describe homotopy structures on topological spaces. The main result of the paper shows that for any such machine one can find an algebraic theory characterizing…
Inspired by the quantitative $K$-theory, in this paper, we introduce the coarse Baum-Connes conjecture with filtered coefficients which generalizes the original conjecture. There are two advantages for the conjecture with filtered…
In this note we consider weighted $(PLB)$-spaces of ultradifferentiable functions defined via a weight function and a weight system, as introduced in our previous work [4]. We provide a complete characterization of when these spaces are…
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…
In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…