  Weakly globular double categories are a model of weak $2$-categories based on
the notion of weak globularity, and they are known to be suitably equivalent to
Tamsamani $2$-categories. Fair $2$-categories, introduced by J. Kock, model
weak $2$-categories with strictly associative compositions and weak unit laws.
In this paper we establish a direct comparison between weakly globular double
categories and fair $2$-categories and prove they are equivalent after
localisation with respect to the $2$-equivalences. This comparison sheds new
light on weakly globular double categories as encoding a strictly associative,
though not strictly unital, composition, as well as the category of weak units
via the weak globularity condition.
