Autonomization of Monoidal Categories

TL;DR

This paper demonstrates that monoidal categories alone suffice for categorical compositional models of natural language, expanding the modeling capabilities in distributional semantics by freely adding adjoints.

Contribution

It introduces a construction that extends monoidal categories with adjoints, enabling more flexible models including non-linear maps and cartesian products.

Findings

Broadened the range of distributional semantics models

Enabled inclusion of non-linear maps and cartesian products

Provided applications to various models of meaning

Abstract

We show that contrary to common belief in the DisCoCat community, a monoidal category is all that is needed to define a categorical compositional model of natural language. This relies on a construction which freely adds adjoints to a monoidal category. In the case of distributional semantics, this broadens the range of available models, to include non-linear maps and cartesian products for instance. We illustrate the applications of this principle to various distributional models of meaning.