Hilbert spaces and C*-algebras are not finitely concrete

• Autoři: LIEBERMAN Michael Joseph; ROSICKÝ Jiří; VASEY Sébastien Bernard
• Rok publikování: 2023
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal of Pure and Applied Algebra
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1016/j.jpaa.2022.107245
• Doi: http://dx.doi.org/10.1016/j.jpaa.2022.107245
• Klíčová slova: Hilbert space; C*-algebra; Faithful functor preserving directed; colimits
• Popis: We show that no faithful functor from the category of Hilbert spaces with injective linear contractions 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*- algebras with *-homomorphisms. This implies, in particular, that this category is not axiomatizable by a first-order theory, a strengthening of a conjecture of Bankston.

Související projekty

• Injektivita a monády v algebře a topologii