I will describe a simple model for the 2-group extensions
of a compact torus by the circle and some familiar contexts in which
these "categorical tori" naturally occur.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/6356