By Michael Lieberman and others

We show that no faithful functor from the category of Hilbert spaces with linear isometries into the category of sets preserves directed colimits. Thus Hilbert spaces cannot form an abstract elementary class, even up to change of language. We deduce an analogous result for the category of commutative unital *C^\ast*-algebras... Show more

September 4, 2019

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Hilbert spaces and ${C}^\ast$-algebras are not finitely concrete

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