Polish spaces of categories enriched over separable Banach spaces

Speaker(s)

Tomasz Kania

Affiliation

Jagiellonian University

Language of the talk

Polish

Date

Dec. 17, 2025, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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We employ the Godefroy--Saint-Raymond machinery of admissible topologies to projectively universal objects in categories such as (separable) Banach spaces, Banach lattices, Banach lattices, C*-algebras etc. as well as countable objects such as groups or rings to study Borel complexity of various naturally occuring properties thereof. 
In the light of the recent result of the speaker, a more common injective approach is not available, e.g., for Banach algebras (there is no universal separable Banach algebra). We will provide illustrative examples of Borel complexity estimation for many more or less familiar properties of the objects in scope. 
The work is based on joint work with J. Swaczyna: 
https://arxiv.org/abs/2508.21242
and two preprints of the speaker:
https://arxiv.org/abs/2511.04314
https://arxiv.org/abs/2510.24441

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