singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom

English

The naturality of the inv_homologyι with respect to f is given by a commutative diagram involving the iCycles and the homology maps.

Русский

Единообразность inv_homologyι по отношению к f задаётся коммутативной диаграммой, содержащей iCycles и гомологии.

LaTeX

$$$(\\mathrm{singleObjHomologySelfIso} \\; c \\; j \\; A)^{-1} \\circ (\\mathrm{homology\\iota}_j) = \\mathrm{oop}$$$

Lean4

@[reassoc (attr := simp)]
theorem singleObjHomologySelfIso_hom_singleObjOpcyclesSelfIso_hom :
    (singleObjHomologySelfIso _ _ _).hom ≫ (singleObjOpcyclesSelfIso _ _ _).hom = ((single C c j).obj A).homologyι j :=
  by
  rw [← cancel_epi (singleObjHomologySelfIso _ _ _).inv, Iso.inv_hom_id_assoc, singleObjHomologySelfIso_inv_homologyι]

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