# Functorial Semantics for Partial Theories

arXiv: https://arxiv.org/abs/2011.06644 · HTML: https://mlsanity.com/paper/2011.06644/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2020.

## Built on by (most cited first, 1 of 1)

- [Lambek pregroups are Frobenius spiders in preorders](https://mlsanity.com/paper/2105.03038/) (2021)

## Abstract (arXiv)

We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of string diagrams as terms. This allows for equational reasoning about the class of models defined by a partial theory. We demonstrate the expressivity of such equational theories by considering a number of examples, including partial combinatory algebras and cartesian closed categories. Moreover, despite the increase in expressivity of the syntax we retain a well-behaved notion of semantics: we show that our categories of models are precisely locally finitely presentable categories, and that free models exist.