instHasShiftOppositeInt — Mathlib

English

Characterization of trW for morphisms in homological kernels.

Русский

Характеризация trW для морфизмов в гомологическом ядре.

LaTeX

$$$F.homologicalKernel.trW f \iff \forall n, IsIso ((F.shift n).map f)$$$

Lean4

/-- The category `Cᵒᵖ` is equipped with the shift such that the shift by `n` on `Cᵒᵖ`
corresponds to the shift by `-n` on `C`. -/
noncomputable scoped instance : HasShift Cᵒᵖ ℤ :=
  (inferInstance : HasShift (OppositeShiftAux C) ℤ)

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