  This work originates from the observation that today's state-of-the-art
statistical language models are impressive not only for their performance, but
also - and quite crucially - because they are built entirely from correlations
in unstructured text data. The latter observation prompts a fundamental
question that lies at the heart of this paper: What mathematical structure
exists in unstructured text data? We put forth enriched category theory as a
natural answer. We show that sequences of symbols from a finite alphabet, such
as those found in a corpus of text, form a category enriched over
probabilities. We then address a second fundamental question: How can this
information be stored and modeled in a way that preserves the categorical
structure? We answer this by constructing a functor from our enriched category
of text to a particular enriched category of reduced density operators. The
latter leverages the Loewner order on positive semidefinite operators, which
can further be interpreted as a toy example of entailment.
