A three-functor formalism for commutative von Neumann algebras

Andre G. Henriques; Thomas A. Wasserman

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arXiv · 2504.10131

A three-functor formalism for commutative von Neumann algebras

Andre G. Henriques·Thomas A. Wasserman

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Abstract

A three-functor formalism is the half of a six-functor formalism that supports the projection and base change formulas. In this paper, we provide a three-functor formalism for commutative von Neumann algebras and their modules. Using the Gelfand-Naimark theorem, this gives rise to a three-functor formalism for measure spaces and measurable bundles of Hilbert spaces. We use this to prove Fell absorption for unitary representations of measure groupoids. The three-functor formalism for commutative von Neumann algebras takes values in W*-categories, and we discuss in what sense it is a unitary three-functor formalism.

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BibTeX RIS

Andre G. Henriques, Thomas A. Wasserman. 2025-04-14. A three-functor formalism for commutative von Neumann algebras. https://arxiv.org/abs/2504.10131

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