This paper presents a formalisation of displayed algebras within UniMath, extending the displayed-category framework to universal algebra. We establish that algebras displayed over a base structure correspond to morphisms into that base, enabling modular development of algebraic constructions. The approach is illustrated through natural examples -- including products, pullbacks, and subalgebras -- and all results are mechanised within univalent foundations. We outline future work integrating this framework more deeply into UniMath and exploring connections with Lawvere theories.

Introducing displayed universal algebra in UniMath / Amato, G., Calosci, M., Maggesi, M., Perini Brogi, C.. - (2025). (Workshop on Homotopy Type Theory/Univalent Foundations 2025 Genoa, Italy 15–16/04/2025).

Introducing displayed universal algebra in UniMath

Perini Brogi Cosimo
2025

Abstract

This paper presents a formalisation of displayed algebras within UniMath, extending the displayed-category framework to universal algebra. We establish that algebras displayed over a base structure correspond to morphisms into that base, enabling modular development of algebraic constructions. The approach is illustrated through natural examples -- including products, pullbacks, and subalgebras -- and all results are mechanised within univalent foundations. We outline future work integrating this framework more deeply into UniMath and exploring connections with Lawvere theories.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/43698
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