Strict stability of extension types
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.07194
- arXiv:
- arXiv:2203.07194
- Bibcode:
- 2022arXiv220307194W
- Keywords:
-
- Mathematics - Category Theory;
- Computer Science - Logic in Computer Science;
- Mathematics - Logic;
- 03B38 (Primary);
- 03G30;
- 18N45;
- 18N50;
- 18N60;
- 55U35 (Secondary);
- F.4.1
- E-Print:
- 16 pages. This text is essentially Chapter 6 from author's PhD thesis arXiv:2202.13132. Addition to acknowledgments. Submitted, but comments welcome!