  We define the bicategory of Graph Convolutional Neural Networks
$\mathbf{GCNN}_n$ for an arbitrary graph with $n$ nodes. We show it can be
factored through the already existing categorical constructions for deep
learning called $\mathbf{Para}$ and $\mathbf{Lens}$ with the base category set
to the CoKleisli category of the product comonad. We prove that there exists an
injective-on-objects, faithful 2-functor $\mathbf{GCNN}_n \to
\mathbf{Para}(\mathsf{CoKl}(\mathbb{R}^{n \times n} \times -))$. We show that
this construction allows us to treat the adjacency matrix of a GCNN as a global
parameter instead of a a local, layer-wise one. This gives us a high-level
categorical characterisation of a particular kind of inductive bias GCNNs
possess. Lastly, we hypothesize about possible generalisations of GCNNs to
general message-passing graph neural networks, connections to equivariant
learning, and the (lack of) functoriality of activation functions.
