Dear Vladimir,

We are also isolated from many and many mathematicians who are trying to find a way to express ideas that in my opinion are most naturally expressed in the UF in various theories formulated inside the set theory.

In this paragraph, are you referring to what Martin called "synthetic homotopy theory/infinity-toposes" branch of the HoTT community, or to a disparate body of mathematical research with different objectives?

Greetings,

Andrew