Related papers: Projective Covers of 2-star-permutable Categories
The number of apparent double points of a smooth, irreducible projective variety $X$ of dimension $n$ in $\Proj^{2n+1}$ is the number of secant lines to $X$ passing through the general point of $\Proj^{2n+1}$. This classical notion dates…
We construct a multiple star product method and by using this method, show that integral forms of some star products can be written in terms of the path-integral. This method can be applied to some examples. Especially, the associativity of…
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In…
This article tackles categorical coherence within a two-dimensional generalization of Lawvere's functorial semantics. 2-theories, a syntactical way of describing categories with structure, are presented. From the perspective here afforded,…
In a series of articles we describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge…
Given an \'etale double covering $\pi\, :\, \widetilde{C}\, \longrightarrow\, C$ of compact Riemannsurfaces with $C$ of genus at least two, we use the Prym variety of the cover to construct canonical projective structures on both…
By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at…
We present an alternative construction of Soergel's category of bimodules associated to a reflection faithful representation of a Coxeter system. We show that its objects can be viewed as sheaves on the associated moment graph. We introduce…
We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective variety up to isomorphism, by using the homological properties of special admissible…
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these…
Following [14], we compute the motivic cohomology ring of the Nisnevich classifying space of the unitary group associated to the standard split hermitian form of a quadratic extension. This provides us with subtle characteristic classes…
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…
Classical Be stars are introduced as object class and their particular potential for space based photometry is highlighted. A brief summary of the various types of variability observed in Be stars makes clear that an interpretation of every…
In this paper I define the notion of a non-degenerate finitely semi-simple semi-strict spherical 2-category of non-zero dimension. Given such a 2-category I define a state-sum for any triangulated compact closed oriented 4-manifold and show…
We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…
We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a monoidal category, which is a version of the "category" of symplectic manifolds and canonical relations obtained by localizing them…
In this note we characterize, within the framework of the theory of finite set, those categories of graphs that are {\em algebraic universal} in the sense that every concrete category embeds in them. The proof of the characterization is…
In this paper, we drive and simplify some important equations and relations for an evolving star with spherical symmetry, and then give some simple analysis for their properties and implications. In the light-cone coordinate system, these…
We propose a new approach to S-protomodular categories in the sense of D. Bourn, N. Martins-Ferreira, A. Montoli, and M. Sobral. Instead of points (=split epimorphisms) it uses generalized points, which we define as composable pairs of…