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Observational note reveals how Kelly's transfinite construction inverts endofunctors, suggesting novel approaches for enriched settings.
In this short note we observe that Kelly's transfinite construction of free algebras yields a way to invert well-pointed endofunctors. In enriched settings, this recovers constructions of Keller, Seidel, and Chen-Wang. We also relate this procedure to localisation by spectra and to Heller's stabilisation.
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