oppositeShiftFunctorAdd_hom_app — Mathlib

English

If a natural transformation τ between F and G is CommShift, then OppositeShift.natTrans.op τ also has a CommShift structure.

Русский

Если натуральное преобразование τ между F и G имеет CommShift, то OppositeShift.natTrans оп τ тоже обладает CommShift.

LaTeX

$$$ \text{CommShift op }(\tau) : OppositeShift.natTrans A ⟶ OppositeShift.natTrans A$ with shift_comm.$$

Lean4

theorem oppositeShiftFunctorAdd_hom_app :
    (shiftFunctorAdd (OppositeShift C A) a b).hom.app X = ((shiftFunctorAdd C a b).inv.app X.unop).op :=
  by
  rw [← cancel_mono ((shiftFunctorAdd (OppositeShift C A) a b).inv.app X), Iso.hom_inv_id_app,
    oppositeShiftFunctorAdd_inv_app, ← op_comp, Iso.hom_inv_id_app, op_id]
  rfl

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