Publication details

Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras


CHIRVASITU Alexandru KO Joanna

Year of publication 2023
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Keywords C*-algebra; W*-algebra; Locally presented; Locally generated; Monadic; Beck’s theorem; Tripleability; Enriched
Description We prove that the forgetful functors from the categories of C?- and W?-algebras to Banach ?-algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosický, and that the categories of unital (commutative) C?-algebras are not locally-isometry ?0-generated either as plain or as metric-enriched categories, answering a question of I. Di Liberti and Rosický. We also prove a number of negative presentability results for the category of von Neumann algebras: not only is that category not locally presentable, but in fact its only presentable objects are the two algebras of dimension ?1. For the same reason, for a locally compact abelian group G the category of G-graded von Neumann algebras is not locally presentable.

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