The topology of critical processes, I (Processes and Models)

TL;DR

This paper introduces a new topological framework for modeling critical, indivisible, and unstoppable processes within directed algebraic topology, aiming to extend the mathematical tools to cover non-reversible and critical phenomena.

Contribution

It establishes a foundational framework for representing critical processes in directed algebraic topology with minimal mathematical prerequisites.

Findings

Defines a new framework for critical processes

Prepares for fundamental category and homology analysis

Extends directed algebraic topology to critical phenomena

Abstract

This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes", indivisible and unstoppable. This introductory article is devoted to fixing the new framework and representing processes of diverse domains, with minimal mathematical prerequisites. The fundamental category and singular homology in the present setting will be dealt with in a sequel.