The paper provides a clear mathematical framework for unifying several recent advances on generalizing CNNs to spaces acted on by groups. The authors make it clear that they do not present any new architectures or fundamentally new mathematics. They are also unapologetic about the fact that the paper is abstract. Having said all this, it is clear that equivariant neural nets are here to stay and writing a paper that provides the right language to talk about them is an important contribution. While the present readership of this might paper might be limited, in the future it might become a standard reference and important stepping stone to designing other types of networks.