Commutative von Neumann algebras

[catdat-issue-creation]

CVNA is complete and cocomplete, but not locally presentable. Its opposite category (compact strictly localizable enhanced measurable spaces) also has interesting properties: it is complete, cocomplete, has a subobject classifier, subobjects form a complete Boolean algebra, is a regular category, but is not a topos.

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This issue has been created by Dmitri Pavlov via the submission form on https://catdat.app/categories

[ScriptRaccoon]

What are good references where all of these properties are proven?

[dmitripavlov]

https://dmitripavlov.org/scans/guichardet.pdf
https://arxiv.org/abs/1202.2994v2
https://mathoverflow.net/questions/384346/is-the-opposite-category-of-commutative-von-neumann-algebras-a-topos