A model for the coherent walking $\ddot{I}‰$-equivalence

Abstract

We prove that a certain $\ddot{I}‰$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $\ddot{I}‰$-equivalence. Further, appropriate truncations of it give models for the fully coherent walking $n$-equivalence for each $n\ge 1$.

20 pages, comments are welcome!