Orientals as free weak ω-categories

Yuki Maehara – 17 February 2021

The orientals were introduced by Street as the free strict ω-categories on simplices. The main result of this work is that they are also the free *weak* ω-categories on the same generating data. More precisely, the complicial nerve of the n-th oriental is a fibrant replacement of Delta[n] in Verity's model structure.