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

Metric enrichment, finite generation, and the path coreflection

“…The earlier [9,Proposition 3.11] says that the category C * c,1 of commutative unital C * -algebras is CMet-tensored. On the other hand, Theorem 4.1 below negates the existence of tensors in C * 1 fairly strongly: in a sense, only the "obvious" ones exist.…”

“…is complete convex (i.e. an object of CCMet) now follows from Theorem 2.21 (e) (completeness) and Corollary 2.24 (convexity): closed connected Riemannian manifolds are convex [24, §7.2, Corollary 2.7], Y is compact, and the infimum (2-9) is achieved by the embedding into X 0 by (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12).…”