Dice Question Streamline Icon: https://streamlinehq.com

Surjectivity of epimorphisms in the category of σ-C*-algebras

Ascertain whether every epimorphism in Cσ, the category of σ-C*-algebras with σ-*-homomorphisms, is surjective.

Information Square Streamline Icon: https://streamlinehq.com

Background

In the ordinary C*-algebra setting, epimorphisms are surjective. For σ-C*-algebras, the authors verify that surjective σ-homomorphisms are epimorphisms but do not know whether the converse holds. Establishing this would align categorical epimorphisms with algebraic surjections in Cσ.

References

Concerning epimorphisms, it is clear that every surjective is an epimorphism. We do not know whether the converse holds too, although this is true in $C$.

— Categories of abstract and noncommutative measurable spaces (2504.13708 - Fritz et al., 18 Apr 2025) in Remark on monomorphisms/epimorphisms (Section on Pedersen–Baire envelopes)