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).
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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]
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
Last revised on May 12, 2023 at 09:03:52. See the history of this page for a list of all contributions to it.