pullbackRightPullbackFstIso_hom_fst

English

If h: W → X is epi and f: X → Y, then pushout.inl(h f) h is iso.

Русский

Если h: W → X эпиморфизм и f: X → Y, то pushout.inl (h ∘ f) h изоморфизм.

LaTeX

$$$\\IsIso(\\mathrm{pushout.inl} (\\mathrm{comp}\\ h f) \\; h)$$$

Lean4

@[reassoc (attr := simp)]
theorem pullbackRightPullbackFstIso_hom_fst :
    (pullbackRightPullbackFstIso f g f').hom ≫ pullback.fst (f' ≫ f) g = pullback.fst f' (pullback.fst f g) :=
  IsLimit.conePointUniqueUpToIso_hom_comp _ _ WalkingCospan.left

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