nLab sound doctrine of limits

1. Idea

A class $\Phi$ of diagram shapes for limits — or more generally a class of weights for limits — is called sound as a doctrine of limits [Adámek, Borceux, Lack & Rosicky (2002)] 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).

2. Definition

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3. References

• Jiří Adámek, Francis Borceux, Stephen Lack, Jiri Rosicky, A classification of accessible categories, Journal of Pure and Applied Algebra 175 1–3 (2002) 7-30 [doi:10.1016/S0022-4049(02)00126-3]

• n-Cafe discussion about the above paper

• C. Centazzo, J. Rosický, E. M. Vitale, A characterization of locally D-presentable categories, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 45 (2004), no. 2, pp. 141-146. numdam.

• 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