| 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 | |