instCommShiftOppositeShiftHomFunctorNatIsoId

English

Instance stating that CommShift holds for OppositeShift.natIsoId hom functor.

Русский

Инстанс, утверждающий, что CommShift выполняется для OppositeShift.natIsoId гом функторa.

LaTeX

$$[NatTrans.CommShift (OppositeShift.natIsoId C A).hom A]$$

Lean4

/-- The natural isomorphism `NatTrans.OppositeShift.natIsoId C A` commutes with shifts.
-/
instance : NatTrans.CommShift (OppositeShift.natIsoId C A).hom A where
  shift_comm
    _ := by
    ext
    dsimp [OppositeShift.natIsoId, Functor.commShiftOp_iso_eq]
    simp only [Functor.commShiftIso_id_hom_app, Functor.comp_obj, Functor.id_obj, Functor.map_id, comp_id,
      Functor.commShiftIso_id_inv_app, CategoryTheory.op_id, id_comp]
    rfl

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