related by the Dold-Kan correspondence
The weak equivalences are the equivalences.
The fibrations are the morphisms that are representably isofibrations, i.e. the morphisms such that is an isofibration for all .
The cofibrations are determined.
We call it the 2-trivial model structure, as it is a 2-categorical analogue of the trivial model structure on any 1-category. It can be said to regard as an (∞,1)-category with only trivial k-morphisms for .
Every object is fibrant and cofibrant.
By duality, any such category has another model structure, with the same weak equivalences but where the cofibrations are the iso-cofibrations and the fibrations are determined. In , the two model structures are the same.
If is an accessible strict 2-monad on a locally finitely presentable strict 2-category . Then the category of strict -algebras admits a transferred model structure from the 2-trivial model structure on . The cofibrant objects therein are the flexible algebras.