nLab
sound doctrine

Idea

A class $\Phi$ of diagram shapes for limits, or more generally a class of weights for limits, is sound if it behaves nicely when paired with the class $\Phi^+$ of all colimit shapes (or weights) that commute with $\Phi$-limits in Set (or more generally in the base of enrichment).

Definition

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References

• Jiri Adamek, Francis Borceux, Stephen Lack, Jiri Rosicky, A classification of accessible categories, web

• n-Cafe discussion about the above paper

• Stephen Lack, Jiri Rosicky, Notions of Lawvere theory, arxiv

• Matěj Dostál, Jiří Velebil, An elementary characterisation of sifted weights, arxiv

• G. M. Kelly, V. Schmitt, Notes on enriched categories with colimits of some class, arXiv