Publication details
Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Pure and Applied Algebra |
| MU Faculty or unit | |
| Citation | |
| Web | |
| Doi | http://dx.doi.org/10.1016/j.jpaa.2022.107209 |
| 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. |