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.
Bibliographical noteFunding Information:
Acknowledgments: We would like to thank Hans Baues and the referee for many useful comments and corrections. The second author wishes to thank the Department of Mathematics of the University of Haifa for their hospitality while holding a postodoral position there during which this work was carried out. This research was supported by BSF grant 2006039.
- Baues-Wirsching cohomology
- Double groupoids
- Simplicially enriched categories
- Track categories
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology