On enriched terms and 2-categorical universal algebra
Category Theory
2025-07-15 v1
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 -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.
Cite
@article{arxiv.2507.09946,
title = {On enriched terms and 2-categorical universal algebra},
author = {Giacomo Tendas},
journal= {arXiv preprint arXiv:2507.09946},
year = {2025}
}