I'm trying to track down a result mentioned in Verdier's Categories Derivees appearing in SGA 4.5. In chapter 2, 3.1 (page 280 in SGA 4.5) Verdier mentions that categorical localisations always exist, and cites [C.G.G] for this result. The problem is, [C.G.G] does not appear anywhere else in SGA 4.5 (in particular, it is not in the bibliography). Does anyone have any idea what paper / book Verdier is referring to here?
2026-03-26 18:58:22.1774551502
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Reference request: localisation of categories
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This is not exactly what you are looking for, but if you only need the fact of existence of localizations, then in his lectures (Wayback Machine) Bertrand Toen shows (see page 3) that localizations of categories exist. Though, for the main part of his proof Toen cites the book by Elmendorf, Kriz, Mandell, May (Wayback Machine).
Here's a guess.
From the bibliography of Schiffmann Gérard's Théorie élémentaire des catégories (1962) which can be found on page 33 of Séminaire Banach (1972):
(It may be hard to find or lost as Chevalley had a habit of only keeping a single copy of his papers.)