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My French is not good enough to be sure about it, but it seems that this paper has the definition you are after.

Evrard, Marcel Fibrations de petites catégories. Bull. Soc. Math. France 103 (1975), no. 3, 241–265. (Numdam)

show/hide this revision's text 1

My French is not good enough to be sure about it, but it seems that this paper has the definition you are after.

Evrard, Marcel Fibrations de petites catégories. Bull. Soc. Math. France 103 (1975), no. 3, 241–265.