The origin of universality: Making and invalidating a free category

Yukio Gunji, Hideki Higashi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We propose a model of evolutionary systems characterized by internal measurement, or endo-physics, that is based on a particular graph morphism. If we take an internal stance, we have to focus on the influence of the outside of the domain of choice. The outside of the domain is not explicitly expressed as a particular ensemble in advance, although a formal expression generally requires an explicit form of the outside as the possible forms. In our model, a system is expressed by a directed graph, and the time transition is expressed as a particular graph morphism referring to the outside of the domain of the morphism. Referring to the outside of the domain is expressed by dynamical decomposition and synthesis of the relationship between a graph and its possible forms expressed as an underlying free category. Because the transformations from a graph to a category and vice versa are expressed as two adjunctive functors, a graph morphism is defined by a sequence of the operation of a free functor and a special operator standing for invalidation of the operation of the free functor. Time development of this system can generate a particular universal structure like a limit and co-limit as a part of a directed graph, which stands for generation of a higher order. We also argue that the process toward the generation of a universal structure can reveal intermittency, and that an emergent boundary in pattern formation can be demonstrated by the generation of this universal structure. In addition, we discuss emergent computation such as the origin of primitive recursive functions through the origination of a universal structure.

Original languageEnglish
Pages (from-to)283-313
Number of pages31
JournalPhysica D: Nonlinear Phenomena
Volume156
Issue number3-4
DOIs
Publication statusPublished - 2001 Aug 15
Externally publishedYes

Fingerprint

Directed graphs
Universality
Morphism
Recursive functions
Functor
Graph in graph theory
Physics
Directed Graph
recursive functions
Decomposition
intermittency
Internal
Colimit
Recursive Functions
Intermittency
Pattern Formation
decomposition
Ensemble
operators
physics

Keywords

  • Category theory
  • Emergent boundary
  • Internal measurement
  • Origin of universality

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

The origin of universality : Making and invalidating a free category. / Gunji, Yukio; Higashi, Hideki.

In: Physica D: Nonlinear Phenomena, Vol. 156, No. 3-4, 15.08.2001, p. 283-313.

Research output: Contribution to journalArticle

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