Tootfinder

Is there an "established" name for the construction in HoTT that associates to every 1-type A the category with A as objects and paths as morphisms, i.e. turns a groupoid (type) into a groupoid (category)?

DHoTT: A Temporal Extension of Homotopy Type Theory for Semantic Drift
Iman Poernomo
https://arxiv.org/abs/2506.09671 https://arxiv.o…

DHoTT: A Temporal Extension of Homotopy Type Theory for Semantic Drift
We introduce Dynamic Homotopy Type Theory (DHoTT), a temporal extension of Homotopy Type Theory (HoTT) designed to reason formally about concepts whose meanings evolve continuously or rupture discontinuously over time. While traditional HoTT captures identity and equivalence within a fixed semantic landscape, DHoTT enriches this framework by explicitly indexing types with a temporal parameter, allowing types themselves to deform, rupture, and reassemble as contexts shift. Formally, we show th…