Talk:Almost ring
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Connection to Gabriel localization
[edit]If m is an idempotent ideal in a commutative unital ring R, the family of ideals containing m is a Gabriel filter. Like all Gabriel filters, an endofunctor of R-Mod is defined, which in this case sends N to Hom( m , Hom( m , N ) ) . It is left-exact, takes R to an R-algebra R^a, takes R-algebras to R^a-algebras, and preserves modules. It is left-adjoint to the inclusion of the subcategory of all N such that N -> Hom( m , N ) is an isomorphism. (These are true for any Gabriel localization.) — Preceding unsigned comment added by Hazelmaye (talk • contribs) 00:58, 18 March 2022 (UTC)
Topoi?
[edit]Remark 4.1.8 of [1] seems cool. Anyone cares to include it? My related post: [2]. --Fourier-Deligne Transgirl (talk) 00:39, 9 November 2022 (UTC)