Related papers: Semi-cubical tribes
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…
A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…
The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to…
In this study we introduce the notions of semi-homotopy of semi-continuous maps and of semi-paths. We also construct a group structure, which will be called semi-fundamental group, using semi-loops and explore some properties of…
We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions…
We prove a triangulation theorem for semi-algebraic sets over a p-adically closed field, quite similar to its real counterpart. We derive from it several applications like the existence of flexible retractions and splitting for…
We construct certain maps from buildings associated to td-groups to a space closely related to the classifying numerable $G$-space for the family $\mathcal{C}$vcy of covirtually cyclic subgroups. These maps are used in forthcoming paper to…
Let $C$ be a smooth, projective and geometrically connected curve defined over a finite field $\mathbb{F}_q(C)$. Given a semisimple $C-S$-group scheme $\underline{G}$ where $S$ is a finite set of closed points of $C$, we describe the set of…
In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…
We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to…
To a tree of semi-simple algebras we associate a qurve (or formally smooth algebra) S. We introduce a Zariski- and etale quiver describing the finite dimensional representations of S. In particular, we show that all quotient varieties of…
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…
The category of Cartesian cubical sets is introduced and endowed with a Quillen model structure using ideas coming from recent constructions of cubical systems of univalent type theory.
We introduce a new cubical model for homotopy types. More precisely, we'll define a category Qs with the following features: Qs is a PROP containing the classical box category as a subcategory, the category Qs-Set of presheaves of sets on…
In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a notion of thin-powered structure on small categories, which…
Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…
We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical…
We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…