functorMap_id — Mathlib

English

There exists an extension l: B_i → Z' with properties f_i ≫ l = t ≫ ι' and l ≫ πZ' = b.

Русский

Существует продолжение l: B_i → Z' с свойствами f_i ≫ l = t ≫ ι' и l ≫ πZ' = b.

LaTeX

$$$ \exists l:\, B_i\to Z' \;\text{such that } f_i\!\gg l = t\gg ι' \wedge l\gg πZ' = b $$$

Lean4

@[simp]
theorem functorMap_id : functorMap f (𝟙 (Arrow.mk πX)) = 𝟙 _ :=
  by
  ext ⟨i, t, b, w⟩
  · simp [functorMap]
  · simp [functorMap, ι_functorMapTgt_assoc f (𝟙 (Arrow.mk πX)) i t b w b (by simp) t (by simp)]

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