dorsal/arxiv
View SchemaOperational Galois adjunctions
| Authors | Bob Coecke, David Moore |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008021 |
| URL | https://arxiv.org/abs/quant-ph/0008021 |
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.
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"abstract": "We present a detailed synthetic overview of the utilisation of categorical\ntechniques in the study of order structures together with their applications in\noperational quantum theory. First, after reviewing the notion of residuation\nand its implementation at the level of quantaloids we consider some standard\nuniversal constructions and the extension of adjunctions to weak morphisms.\nSecond, we present the categorical formulation of closure operators and\nintroduce a hierarchy of contextual enrichments of the quantaloid of complete\njoin lattices. Third, we briefly survey physical state-property duality and the\ncategorical analysis of derived notions such as causal assignment and the\npropagation of properties.",
"arxiv_id": "quant-ph/0008021",
"authors": [
"Bob Coecke",
"David Moore"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"title": "Operational Galois adjunctions",
"url": "https://arxiv.org/abs/quant-ph/0008021"
},
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