nLab Yemon Choi

Interloper/dilettante. “Functional analyst”, who sometimes wonders if the term meant something different in Britain that it does in North America. Keeps finding category-theoretic things all over the place in old analysis, never mind the brave new world of NCG, and is starting to feel that they should be collated somewhere.

• website

(Last properly active in 2014, but might be returning in 2021…)

To do list

Some things I am considering trying to write about, or contribute to. (This is mainly meant as a list to remind or nag me to write things down.)

• projective, injective and flat Banach spaces (both in the metric and topological categories of Banach spaces)
• RKHS
• the bidualization monad on Banach spaces
• Kaijser and Wick-Pelletier’s work on interpolation
• Arens-Eells spaces, a.k.a. the adjunction between Banach spaces and metric spaces.
• Richard Arens’s paper using “phyla”, or: where Banach algebras and symmetric monoidal categories should have met. (There is now some stuff on Arens products on the Banach algebras page.)
• Categori(c)al basics of operator spaces: MAX, MIN, and various tensor products
• functorial aspects of the group von Neumann algebra construction
• dual Banach algebras

A survey paper which is more rewarding than this page

J.M.F. Castillo. The hitchhiker guide to categorical Banach space theory. Part I. Extracta Math. 25(2) (2010), 103–149.

(Currently freely available on the journal’s website )

category: people