Related papers: Generalized covering space theories
For an internal category $\mathbb{C}$ in a cartesian category $\mathcal{C}$ we define, naturally in objects $X$ of $\mathcal{C}$, $Prin_{\mathbb{C}}(X)$. This is a category whose objects are principal $c \mathbb{C}$-bundles over $X$ and…
Homotopy type theory is a formal language for doing abstract homotopy theory -- the study of identifications. But in unmodified homotopy type theory, there is no way to say that these identifications come from identifying the path-connected…
We construct injective hulls and projective covers in categories of generalized uniform hypergraphs which generalizes the constructions in the category of quivers and the category of undirected graphs. While the constructions are not…
As the first part of the treatise on A General Theory of Concept Lattice (I-V), this work develops the general concept lattice for the problem concerning categorization of objects according to their properties. Unlike the conventional…
We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we introduce a cohomology theory based on measurable cochains which are continuous in a neighbourhood of…
We give a proof of the existence of generalized definable locally compact models for arbitrary approximate subgroups via an application of topological dynamics in model theory. Our construction is simpler and shorter than the original one…
For a (possibly large) realized limit sketch $\mathcal{S}$ such that every $\mathcal{S}$-model is small in a suitable sense we show that the category of cocontinuous functors $\mathsf{Mod}(\mathcal{S}) \to \mathcal{C}$ into a cocomplete…
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two projective bundle structures. Given a general hyperplane section on such a variety, we consider…
In Categorial Topology, given a category (as a "geometric object") we can consider its properties preserved under continuous action (a "deformation") of a comma-propagation operation. However, the Metacategory space, valid for all…
Let $Conf^{lf}_{\infty}(\C)$ and $C^{lf}_{\infty}(\C)$ denote the locally finite infinite ordered and unordered configuration spaces of the complex plane. We prove that both $Conf^{lf}_{\infty}(\C)$ and $C^{lf}_{\infty}(\C)$ are aspherical.…
Broadly speaking the present is a homotopy complement to the book of Giraud, albeit in a couple of different ways. In the first place there is a representability theorem for maps to a topological champ (a.k.a. stack) and whence an extremely…
In this paper we introduce and study the so-called continuous $K$-theory for a certain class of "large" stable $\infty$-categories, more precisely, for dualizable presentable categories. For compactly generated categories, the continuous…
Consider a finite, regular cover $Y\to X$ of finite graphs, with associated deck group $G$. We relate the topology of the cover to the structure of $H_1(Y;\mathbb{C})$ as a $G$-representation. A central object in this study is the {\em…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
We develop foundations for the category theory of $\infty$-categories parametrized by a base $\infty$-category. Our main contribution is a theory of indexed homotopy limits and colimits, which specializes to a theory of $G$-colimits for $G$…
In the sixties, Grothendieck developed the theory of pro-objects over a category. The fundamental property of the category $Pro(C)$ is that there is an embedding $C \stackrel{c}{\rightarrow} Pro(C)$, $Pro(C)$ is closed under small…
For a finite group $G$, let $\H_{g,G,\xi}$ be the stack of admissible $G$-covers $C\to D$ of stable curves with ramification data $\xi$, $g(C)=g$ and $g(D)=g'$. There are source and target morphisms $\phi\colon \H_{g,G,\xi}\to \M_{g,r}$ and…
A principal torus bundle over a complex manifold with even dimensional fiber and characteristic class of type $(1,1)$ admits a family of regular generalized complex structures (GCS) with the fibers as leaves of the associated symplectic…
A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups $\mathscr{U}$. Global representations assemble into an abelian category…
By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these…