toFun — Mathlib

English

Analogous to mkQ for the right tensor, there is a correspondence between the kernel of rTensor Q N.mkQ and the image of rTensor Q N.subtype.

Русский

Аналогично для правого тензора определения ядра и образа через N-subtype.

LaTeX

$$ker( rTensor Q N.mkQ ) = range( rTensor Q N.subtype )$$

Lean4

/-- The direct map in `rTensor.equiv` -/
noncomputable def toFun (hfg : Exact f g) : N ⊗[R] Q ⧸ range (rTensor Q f) →ₗ[R] P ⊗[R] Q :=
  Submodule.liftQ _ (rTensor Q g) <| by
    rw [range_le_iff_comap, ← ker_comp, ← rTensor_comp, hfg.linearMap_comp_eq_zero, rTensor_zero, ker_zero]

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