Talk:Almost ring

Connection to Gabriel localization
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?
Remark 4.1.8 of seems cool. Anyone cares to include it? My related post:. --Fourier-Deligne Transgirl (talk) 00:39, 9 November 2022 (UTC)