preservesHomology_preadditiveCoyonedaObj_of_projective

English

If P is a projective object in an abelian category, then the preadditive Co-Yoneda functor at P preserves homology.

Русский

Если P — проективный объект в абелевой категории, то преддобавительная ко-ёнеда-функтор в P сохраняет гомологию.

LaTeX

$$$ (\text{preadditiveCoyonedaObj}(P)).\mathrm{PreservesHomology} $$$

Lean4

/-- The preadditive Co-Yoneda functor on `P` preserves homology if `P` is projective. -/
noncomputable instance preservesHomology_preadditiveCoyonedaObj_of_projective (P : C) [hP : Projective P] :
    (preadditiveCoyonedaObj P).PreservesHomology :=
  by
  haveI := (projective_iff_preservesEpimorphisms_preadditiveCoyonedaObj P).mp hP
  apply Functor.preservesHomology_of_preservesEpis_and_kernels

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