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October 2, 2025Open Access

On enriched terms and 2-categorical universal algebra

Key Points

The new enriched terms generalize previous notions, creating a broad framework for interpretability in algebra.
An explicit description of free structures is provided, alongside a proof of a 2-dimensional Birkhoff variety theorem.
This research focuses on 2-dimensional terms and equational theories, contributing to the field of universal algebra.
The enhancements in term-interpretability extend applications to various mathematical structures including posets and metric spaces.

Abstract

We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosický. These new terms come together with a notion of term-interpretability, which recovers the same type of interpretability that has been considered for enrichment over posets, metric spaces, and ω-complete posets. As an application of this, we specialize to the 2-categorical case by considering 2-dimensional terms and 2-dimensional equational theories. In this context we also give an explicit description of free structures and prove a 2-dimensional Birkhoff variety theorem.

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Cite This Study

Giacomo Tendas (Mon,) studied this question.

synapsesocial.com/papers/68de68e583cbc991d0a20f70 https://doi.org/https://doi.org/10.48550/arxiv.2507.09946