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[Merged by Bors] - feat(category_theory/sites/{sheaf, sheafification}): monomorphisms of sheaves are precisely monomorphisms of presheaves#15932
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erdOne
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I think these results are all done in one form or the other in mathlib.
Still, the lemmas in the morphism level should still be useful, but probably should go in
category_theory.sites.sheafification instead.
Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
…prover-community/mathlib into jjaassoonn/epi_mono_sheaves
erdOne
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Aug 10, 2022
Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
jcommelin
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Aug 10, 2022
| hom_equiv_naturality_right' := λ P Q R η γ, by { dsimp, rw category.assoc } } | ||
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| instance Sheaf_to_presheaf_preserves_mono : (Sheaf_to_presheaf J D).preserves_monomorphisms := | ||
| functor.preserves_monomorphisms_of_adjunction (sheafification_adjunction _ _) |
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I think that providing the right adjoint instance as @erdOne suggested is the better approach.
The rest looks good to me.
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… sheaves are precisely monomorphisms of presheaves (#15932) * monomorphisms of sheaves are precisely monomorphisms of underlying presheaves (when presheaves can be sheafified) * a morphism between sheaves is epic if the morphism between underlying presheaves is epic. (The converse is not always true)
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