Publication details

Discrete equational theories

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Year of publication 2024
Type Article in Periodical
Magazine / Source Mathematical Structures in Computer Science
MU Faculty or unit

Faculty of Science

Keywords Enriched equational theory; enriched monad; Birkhoff subcategory
Description On a locally $\lambda$-presentable symmetric monoidal closed category $\mathcal {V}$, $\lambda$-ary enriched equational theories correspond to enriched monads preserving $\lambda$-filtered colimits. We introduce discrete $\lambda$-ary enriched equational theories where operations are induced by those having discrete arities (equations are not required to have discrete arities) and show that they correspond to enriched monads preserving preserving $\lambda$-filtered colimits and surjections. Using it, we prove enriched Birkhof-type theorems for categories of algebras of discrete theories. This extends known results from metric spaces and posets to general symmetric monoidal closed categories.
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