  We provide a construction for categorical representation learning and
introduce the foundations of "$\textit{categorifier}$". The central theme in
representation learning is the idea of $\textbf{everything to vector}$. Every
object in a dataset $\mathcal{S}$ can be represented as a vector in
$\mathbb{R}^n$ by an $\textit{encoding map}$ $E:
\mathcal{O}bj(\mathcal{S})\to\mathbb{R}^n$. More importantly, every morphism
can be represented as a matrix $E:
\mathcal{H}om(\mathcal{S})\to\mathbb{R}^{n}_{n}$. The encoding map $E$ is
generally modeled by a $\textit{deep neural network}$. The goal of
representation learning is to design appropriate tasks on the dataset to train
the encoding map (assuming that an encoding is optimal if it universally
optimizes the performance on various tasks). However, the latter is still a
$\textit{set-theoretic}$ approach. The goal of the current article is to
promote the representation learning to a new level via a
$\textit{category-theoretic}$ approach. As a proof of concept, we provide an
example of a text translator equipped with our technology, showing that our
categorical learning model outperforms the current deep learning models by 17
times. The content of the current article is part of the recent US patent
proposal (patent application number: 63110906).
