nLab pseudosimplicial object

Given a 2-category (strict 2-category or bicategory) $C$, the pseudosimplicial object in $C$ is a pseudofunctor, that is a 2-functor $\Delta^{op}\to C$ in the pseudosense (associativity coherences preserved up to invertible 2-cells), and where the category of finite ordinals and monotone maps $\Delta$ is viewed as a 1-category or equivalently a 2-category with only trivial 2-cells. For example, we can consider pseudosimplicial categories.

See also pseudocoherence?.