DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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Conical enriched limit

Definition

Assume $V$ is symmetric monoidal right closed, locally small, complete, and cocomplete.

Let $K$ be a small ordinary category and let $D : K \to B_{0}$ be an ordinary diagram in the underlying category of a $V$ -category $B$ .

Using The free enriched category is left 2-adjoint to the underlying-category construction, regard $D$ as the same data as a $V$ -functor $\tilde{D} : K_{V} \to B$ . A conical enriched limit of $D$ is the enriched weighted limit of $\tilde{D}$ by the constant weight at the tensor unit $1$ .

So conical enriched limits are the enriched limits whose weight carries no extra indexing data beyond the ordinary shape $K$ .

Depends on

Used by

Dependency tree · two levels

9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

G. M. Kelly, Basic Concepts of Enriched Category Theory, Section 3.8 (standard reference, not scraped)
Emily Riehl, Categorical Homotopy Theory, Section 7.5 (standard reference, not scraped)