Strict stability of extension types
We show that the extension types occurring in Riehl--Shulman's work on synthetic $(\infty,1)$-categories can be interpreted in the intended semantics in a way so that they are strictly stable under substitution. The splitting method used here is due to Voevodsky in 2009. It was later generalized by Lumsdaine--Warren to the method of local universes.
- Pub Date:
- March 2022
- Mathematics - Category Theory;
- Computer Science - Logic in Computer Science;
- Mathematics - Logic;
- 03B38 (Primary);
- 55U35 (Secondary);
- 16 pages. This text is essentially Chapter 6 from author's PhD thesis arXiv:2202.13132. Addition to acknowledgments. Submitted, but comments welcome!