More on soundness in the enriched context

2024/08/31 by Tendas, Giacomo · 1 citation
#18C05 #18C15 #18C35 #18D20 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.00389

Abstract

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

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• On enriched terms and 2-categorical universal algebra

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