Definition Coherent Nerve [efr-FG0T]

Let \mathcal {C} be a 2-category with finite 2-limits and 2-colimits. Let X be a pseudocategory object in \mathcal {C}. Then, viewing the finite ordinals [n] as categories, we obtain for each n an object of \mathcal {C} classifying (normal) pseudofunctors [n] \to X. These assemble into a (strict) simplicial object which we denote N(X) \in [\Delta ^\mathrm {op},\mathcal {C}] and call the coherent nerve of X.