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arXiv · 2409.00389

More on soundness in the enriched context

Giacomo Tendas
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Abstract

Working within enriched category theory, we further develop the use of soundness, introduced by Ad\'amek, Borceux, Lack, and Rosick\'y for ordinary categories. In particular we investigate: (1) the theory of locally $\Phi$-presentable $\mathcal V$-categories for a sound class $\Phi$, (2) the problem of whether every $\Phi$-accessible $\mathcal V$-category is $\Psi$-accessible, for given sound classes $\Phi\subseteq\Psi$, and (3) a notion of $\Phi$-ary equational theory whose $\mathcal V$-categories of models characterize algebras for $\Phi$-ary monads on $\mathcal V$.

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Giacomo Tendas. 2024-08-31. More on soundness in the enriched context. https://doi.org/10.1016/j.jpaa.2025.108110

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