Operational Galois adjunctions
Abstract
We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its implementation at the level of quantaloids we consider some standard universal constructions and the extension of adjunctions to weak morphisms. Second, we present the categorical formulation of closure operators and introduce a hierarchy of contextual enrichments of the quantaloid of complete join lattices. Third, we briefly survey physical state-property duality and the categorical analysis of derived notions such as causal assignment and the propagation of properties.
Cite
@article{arxiv.quant-ph/0008021,
title = {Operational Galois adjunctions},
author = {Bob Coecke and David Moore},
journal= {arXiv preprint arXiv:quant-ph/0008021},
year = {2007}
}
Comments
24 pages - survey with proofs; Chapter of the volume: 'Current Research in Operational Quantum Logic: Algebras, Categories, Languages', Fundamental Theories of Physics 111, Kluwer Academic Publishers (2000); edited by Bob Coecke, David Moore and Alex Wilce pp. 195-218