标题： 一种关于交换冯·诺伊曼代数的三函子形式主义 显示英文标题

标题： A three-functor formalism for commutative von Neumann algebras

摘要： 一个三函子形式主义是六函子形式主义的一半，支持投影公式和基变更公式。 本文中，我们为交换冯·诺依曼代数及其模提供了三函子形式主义。 利用盖尔芳特-奈马克定理，这导致了测度空间和希尔伯特空间可测丛的三函子形式主义。 我们用它来证明测度群oid的酉表示的费尔吸收。 交换冯·诺依曼代数的三函子形式主义取值于W*范畴，并且我们讨论了它在何种意义上是一种酉三函子形式主义。 显示英文摘要

摘要： 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.