22 нояб. 2023 г. · Homotopy type theory provides a synthetic formalization of homotopy theory in its modern and most powerful incarnation in the guise of (∞,1)- ...

24 сент. 2024 г. · The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT).

Synthetic homotopy theory is the name given to studying ∞-groupoids in their own terms, i.e., the application of homotopy type theory to computing homotopy ...

24 сент. 2024 г. · The goal of this dissertation is to present results from synthetic homotopy theory based on homotopy type theory (HoTT).

20 янв. 2020 г. · Homotopy type theory is an extension of type theory that enables synthetic reasoning about spaces and homotopy the- ory. This has led to elegant ...

12 апр. 2024 г. · We begin our journey into synthetic homotopy theory by translating the notions of truncatedness and connectedness into type theory. We also ...

14 мар. 2022 г. · Basics of type theory. Identity types. Homotopy type theory. Synthetic homotopy theory. Summary. References. Synthetic homotopy groups.

Homotopy theory can be developed synthetically in homotopy type theory, using types to describe spaces, the identity type to describe paths in a space, ...

Synthetic homotopy theory. Content created by Egbert Rijke, Fredrik Bakke, Vojtěch Štěpančík, Tom de Jong, Raymond Baker and Jonathan Prieto-Cubides.

Homotopy type theory provides another way to do abstract homotopy theory. It feels even more synthetic because the framework ensures that everything is ...