TL;DR
This paper introduces two-track categories, a 2-dimensional extension of track categories, and develops a cohomology theory to classify their extensions, advancing the modeling of categories enriched in 2-type spaces.
Contribution
It defines two-track categories and a cohomology theory for classifying their extensions, providing new tools for higher-dimensional category modeling.
Findings
Two-track categories model categories enriched in 2-type spaces
A Baues-Wirsching type cohomology theory for track categories is developed
The cohomology theory classifies two-track extensions of track categories
Abstract
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 D by a module over D.
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