annihilator and ideal sheaves#3
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Introduce the annihilator ideal sheaf of a sheaf of modules over a general site, formulated in the language of (pre)sheaves of modules. - `PresheafOfModules.SubmoduleSystem`: a restriction-stable family of submodules of a presheaf of modules, cutting out a subobject (`toPresheafOfModules`) with its inclusion monomorphism (`ι`). - `PresheafOfModules.annihilatorIdeal`/`annihilator`: the local annihilator (sections of `R` whose every restriction annihilates `M`), a subobject of the unit, with `mem_annihilatorIdeal` and the contravariance lemma `annihilatorIdeal_le_of_surjective`. - `SheafOfModules.annihilator`: the annihilator as a sheaf of modules, together with its monomorphism into `unit R`. The sheaf condition is proved by the covering-closure argument for the underlying subpresheaf of the sheaf `R`. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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