hasProjectiveDimensionLT_zero — Mathlib

English

The opposite of the inverse of imageUnopOp g composed with the opposite of the image factor through g equals the image morphism of g.

Русский

Обратная imageUnopOp g после композиции с противоположной частью через образ g равна образу g.

LaTeX

$$$ (\mathrm{imageUnopOp}\, g)^{\mathrm{inv}} \circ (\mathrm{factorThruImage}\, g^{\mathrm{unop}})^{op} = \mathrm{image}.\iota\, g $$$

Lean4

theorem hasProjectiveDimensionLT_zero (hX : IsZero X) : HasProjectiveDimensionLT X 0 :=
  by
  letI := HasExt.standard C
  rw [hasProjectiveDimensionLT_iff]
  intro i hi Y e
  rw [← e.mk₀_id_comp, hX.eq_of_src (𝟙 X) 0, Ext.mk₀_zero, Ext.zero_comp]

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