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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更多关于丰富背景下的健全性问题
在丰富范畴理论中,我们进一步发展了由阿德梅克(Ad\'amek)、博尔科(Borceux)、拉克(Lack)和罗西克(Rosick\'y )针对普通范畴引入的声音的使用。我们特别研究了(1) 对于声类$\Phi$,局部$\Phi$可呈现的$\mathcal V$类的理论,(2) 是否每个$\Phi$可进入的$\mathcal V$类都是($\Psi$可进入的)问题、(3) $\Phi$-ary 等式理论的运动,其模型的 $\mathcal V$ 类别描述了 $\mathcal V$ 上 $\Phi$-ary 单子的代数式。
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