Related papers: Category bases that are equivalent to topologies

I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…

Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that…

We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…

By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…

We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…

Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

We prove, over any base ring, that the infinity-category of strictly unital A-infinity-categories (and strictly unital functors) is equivalent to the infinity-category of unital A-infinity-categories (and unital functors). We also identify…

In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These…

Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…

We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…

A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…

In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…

In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose…

Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…

The recent trend in mathematics is towards a framework of abstract mathematical objects, rather than the more concrete approach of explicitly defining elements which objects were thought to consist of. A natural question to raise is whether…

We present a necessary and sufficient condition for the topological equivalence of a continuous function on a plane to a projection onto one of coordinates.

Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…