Filtering germs: Groupoids associated to inverse semigroups

Armstrong, Becky; Clark, Lisa Orloff; Huef, Astrid an; Jones, Malcolm; Lin, Ying Fen

doi:10.1016/j.exmath.2021.07.001

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2024

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Cited by 4 publications

(2 citation statements)

References 20 publications

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“…Example 8 Geometric structure of the lab wall of Example 7 can be described by letting W be the object space G 0 of a Lie groupoid G that encodes local symmetries of the wall, e.g., such that each arrow g ∶ x → y is a specification of how to map neighborhoods of x into "similar" neighborhoods of y (cf. étale groupoids associated to inverse semigroups, in [3] and references therein). The measurement space O(G) is classical, and again W plays the role of state space, now equipped with "dynamics" provided by the groupoid structure.…”

Section: Groupoidsmentioning

confidence: 99%

An Abstract Theory of Physical Measurements

Resende

2021

Found Phys

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The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced. This translates into an algebraic and topological definition of measurement space that caters for the distinction between quantum and classical measurements and allows a notion of observer to be derived.

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Section: Groupoidsmentioning

confidence: 99%

An Abstract Theory of Physical Measurements

Resende

2021

Found Phys

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“…In a nutshell noncommutative Stone duality associates to an ample groupoid G the Boolean inverse semigroup of its compact open local bisections Γ (G ). Various filter constructions can be employed to describe the converse operation [1,14,18].…”

Section: Introductionmentioning

confidence: 99%