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Ari Rosenfield (Jan 15 2025 at 23:57):Hi, this is my first post ever! Does anyone here know of a reference discussing the free completion with respect to finite weighted limits of an enriched category (where the enriching category is sufficiently "nice;" i.e. closed symmetric monoidal, locally finitely presentable, etc.)?
Either an explicit construction or an argument for its existence would do.
Nathanael Arkor (Jan 16 2025 at 00:26):The usual reference would be Theorem 5.35 of Kelly's Basic Concepts of Enriched Category Theory, which gives the construction more generally for a given class of weights.