From Concurrency to Algebraic Topology

From Concurrency to Algebraic Topology

This paper is a survey of the new notions and results scattered in [13,11,12]. However the speculations of Section 5 and Section 6 are new. Starting from a formalization of higher dimensional automata (HDA) by strict globular ω-categories, the construction of a diagram of simplicial sets over the three-object small category − ← gl → + is exposed. Some of the properties discovered so far on the ...

Algebraic topology and concurrency

1. Introduction This article is intended to provide some new insights about concurrency theory using ideas from geometry, and more speciically from algebraic topology. The aim of the paper is twofold: we justify applications of geometrical methods in concurrency through some chosen examples and we give the mathematical foundations needed to understand the geometric phenomenon that we identify. ...

Concurrency and Directed Algebraic Topology

Categorically-algebraic topology and its applications

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

Introduction to Applied Algebraic Topology