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A category of quantum posets | | Andre Kornell
; Bert Lindenhovius
; Michael Mislove
; | | Date: |
27 Jan 2021 | | Abstract: | We define a quantum poset to be a hereditarily atomic von Neumann algebra
equipped with a quantum partial order in Weaver’s sense. These quantum posets
form a category that is complete, cocomplete and symmetric monoidal closed.
This yields a quantum analogue of the inclusion order on a powerset. We show
that every quantum poset can be embedded into its powerset via a quantum
analogue of the mapping that takes each element of a poset to its down set. | | Source: | arXiv, 2101.11184 | | Services: | Forum | Review | PDF | Favorites | |
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