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2c7d975 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | import Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
import Mathlib.Algebra.Homology.ShortComplex.ExactFunctor
import Mathlib.Algebra.Homology.ShortComplex.ModuleCat
namespace OAI
open CategoryTheory
namespace ArExplicit.ModuleRestriction
universe v u u'
variable {R : Type u} {S : Type u'} [Ring R] [Ring S] (f : R →+* S)
theorem map_exact (s : ShortComplex (ModuleCat.{v} S)) (h : s.Exact) :
(s.map (ModuleCat.restrictScalars f)).Exact := by
rw [ShortComplex.ShortExact.moduleCat_exact_iff_function_exact] at h ⊢
exact h
noncomputable instance preservesHomology : (ModuleCat.restrictScalars.{v} f).PreservesHomology :=
((Functor.exact_tfae (ModuleCat.restrictScalars.{v} f)).out 2 3).mp (map_exact f)
end ArExplicit.ModuleRestriction
end OAI
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