Simulations as Homotopies

We exhibit a model structure on 2-Cat, obtained by transfer from sSet across the adjunction C2 ◦ Sd a Ex ◦ N2. A certain class of homotopies in this model structure turns out to be in 1-to-1 correspondence with strong simulations among labeled transitions systems, formalising the geometric intuition of simulations as deformations. The correspondence still holds in the cubical setting, characterising simulations of higher-dimensional transition systems (HDTS).