I have recently learned a bit about higher category theory. And there is a question I would like to ask. Can we enrich banach space interpolation theory by using higher category theory?

Is it possible to get new insight into this theory using higher categories?

In particular, it seems interesting to me to reformulate banach space interpolation theorems in categorical language.

For example, how can I rewrite the reiteration theorem in terms of a functor acting in one category? Here, reiteration theorem is a theorem in banach space interpolation theory which states that there is no use of applying the interpolation functor twice.

I know my questions may seem vague or fuzzy. But anyway,I hope to hear to get an answer soon.