Related papers: Various topos of types constructions

We give new bounds on the Erdos-Szekeres theorems for convex bodies of Bisztriczky and Fejes Toth and of Pach and Toth. We derive them from a combinatorial characterization of convex position of a family of planar convex bodies. This…

In order to make the fundamental group, one of the most well known invariants in algebraic topology, more useful and powerful some researchers have introduced and studied various topologies on the fundamental group from the beginning of the…

Our main theorem is that the inclusion of a Birkhoff variety in the affine Grassmannian is a homotopy equivalence. We also construct analogues of tubular neighborhoods for Birkhoff and Schubert varieties. We include some observations on…

The study of the topology of polynomial maps originates from classical questions in affine geometry, such as the Jacobian Conjecture, as well as from works of Whitney, Thom, and Mather in the 1950-70s on diffeomorphism types of smooth maps.…

We review definitions and basic properties of operads, PROPs and algebras over these structures.

This is the second chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.

We survey recent developments on mapping class groups of surfaces of infinite topological type.

Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…

A Hopf monoid (in Joyal's category of species) is an algebraic structure akin to that of a Hopf algebra. We provide a self-contained introduction to the theory of Hopf monoids in the category of species. Combinatorial structures which…

This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…

We construct a six-dimensional Maxwell theory using a latticized extra space, the continuum limit of which is a shifted torus recently discussed by Dienes. This toy model exhibits the correspondence between continuum theory and discrete…

Normally we judge Topological shapes analytically but they hide significant amount of data in them about coordinate planes and ordered & unordered paris. In this article we will build our intuition and find those datas.

We study possibilities of preservations for properties, their links and related connections between semantic and syntactic ones, both in general and as characterizations for subalgebras, congruence relations, Henkin construction,…

We construct $W$-types in the category of coalgebras for a cartesian comonad. It generalizes the constructions of $W$-types in presheaf toposes and gluing toposes.

We give interpretations of some known key agreement protocols in the framework of category theory and in this way we give a method of constructing of many new key agreement protocols.

This paper supplements [17], showing that categorically the layered theory is the same as the theory of ordered monoids (e.g. the max-plus algebra) used in tropical mathematics. A layered theory is developed in the context of categories,…

We describe an Aldous--Hoover-type characterization of random relational structures that are exchangeable relative to a fixed structure which may have various equivalence relations. Our main theorem gives the common generalization of the…

We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.

We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities…

The species of finite topological spaces admits two graded bimonoid structures, recently defined by F. Fauvet, L. Foissy, and the second author. In this article, we define a doubling of this species in two different ways. We build a…