A folk model structure on omega-cat

Yves Lafont (1) , François Métayer (2) , Krzysztof Worytkiewicz (3)

1 IML - Institut de mathématiques de Luminy
2 PPS - Preuves, Programmes et Systèmes
3 Katedra Informatyki

The primary aim of this work is an intrinsic homotopy theory of strict $\omega$-categories. We establish a model structure on $\omega$-Cat, the category of strict $\omega$-categories. The constructions leading to the model structure in question are expressed entirely within the scope of $\omega$-Cat, building on a set of generation cofibrations and a class of weak equivalences as basic items.

Mots clés: homotopy; model structure; n-category

Domaines: Catégories et ensembles [math.CT]

Yves Lafont, François Métayer, Krzysztof Worytkiewicz. A folk model structure on omega-cat. Advances in Mathematics, 2010, 224 (3), pp.1183-1231. ⟨10.1016/j.aim.2010.01.007⟩. ⟨hal-00395898⟩