cyclesOpIso — Mathlib

English

There is an isomorphism cyclesOpIso: S.op.cycles ≅ Opposite.op S.opcycles, when S has right homology.

Русский

Существует изоморфизм cyclesOpIso: S.op.cycles ≅ Opposite.op S.opcycles, если у S есть правая гомология.

LaTeX

$$S.op.cycles ≅ Opposite.op S.opcycles$$

Lean4

/-- The cycles in the opposite category of the opposite of a short complex identifies
to the opcycles of this short complex. -/
noncomputable def cyclesOpIso [S.HasRightHomology] : S.op.cycles ≅ Opposite.op S.opcycles :=
  S.rightHomologyData.op.cyclesIso

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