We describe a 2-dimensional analogue of track categories, called two-track categories, and show that it can be used to model categories enriched in 2-type mapping spaces. We also define a Baues-Wirsching type cohomology theory for track categories, and explain how it can be used to classify two-track extensions of a track category by a module over.
- Baues-Wirsching cohomology
- Double groupoids
- Simplicially enriched categories
- Track categories