pullbackComparison_comp_fst — Mathlib

English

The mapLift for i' i equals a coherence morphism composed with mapLift i' and mapLift f g i.

Русский

MapLift для i' i равен композиции когерентного морфизма, затем mapLift i', и mapLift f g i.

LaTeX

$$$\mathrm{pushout.mapLift} f g (i'\, i) = (\mathrm{pushout.congrHom} (\mathrm{Category.assoc} _ _ _) (\mathrm{Category.assoc} _ _ _)).hom \\;\; \;\; \mathrm{pushout.mapLift} _ _ i' \\; \; \mathrm{pushout.mapLift} f g i$$$

Lean4

@[reassoc (attr := simp)]
theorem pullbackComparison_comp_fst (f : X ⟶ Z) (g : Y ⟶ Z) [HasPullback f g] [HasPullback (G.map f) (G.map g)] :
    pullbackComparison G f g ≫ pullback.fst _ _ = G.map (pullback.fst f g) :=
  pullback.lift_fst _ _ _

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