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arXiv · 2507.09946

On enriched terms and 2-categorical universal algebra

Giacomo Tendas
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Abstract

We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosick\'y. 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 $\omega$-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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Giacomo Tendas. 2025-07-14. On enriched terms and 2-categorical universal algebra. https://arxiv.org/abs/2507.09946

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