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Gray-categories model algebraic tricategories
Theory and applications of categories, Tome 38 (2022), pp. 1136-1155.

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Lack described a Quillen model structure on the category GrayCat of Gray-categories and Gray-functors, for which the weak equivalences are the weak 3-equivalences. Restricted to Gray-groupoids, the resulting homotopy category is equivalent to the homotopy category of 3-types. In this note, we adapt the technique of Gurski, Johnson, and Osorno to show the localization of GrayCat at the weak equivalences is equivalent to the category of algebraic tricategories and pseudo-natural equivalence classes of weak 3-functors. This finishes establishing the homotopy hypothesis for algebraic trigroupoids.
Publié le :
Classification : 18N20 and 18N40
Keywords: Gray-categories, algebraic tricategories, homotopy hypothesis 
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     author = {Giovanni Ferrer},
     title = {Gray-categories model algebraic tricategories},
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Giovanni Ferrer. Gray-categories model algebraic tricategories. Theory and applications of categories, Tome 38 (2022), pp. 1136-1155. http://geodesic.mathdoc.fr/item/TAC_2022_38_a28/